Abstract group data - 77760.bo

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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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 120, 'aut_gen_orders': [12, 12, 30, 30, 12], 'aut_gens': [[138389, 316920, 3634559, 243, 85805, 93924236159, 80880], [357834, 224515, 40002955, 243, 5309, 374183798155, 45363], [321841, 243, 3714605, 143975, 322558, 275469551405, 281788], [5611, 143975, 40055042, 45504, 5161, 449307267842, 148], [138389, 224515, 186814610397, 80644, 5309, 174919403997, 80880], [357362, 45504, 448908047405, 143975, 40892, 274072463405, 281788]], 'aut_group': None, 'aut_hash': 4510848913879562672, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 311040, 'aut_permdeg': 48, 'aut_perms': [2588095353240936216573826954757746300612836352373993210025010, 1671304204921840573303920166558378664303977009252648507248776, 10141641032926069761490728046281796800451983427719401426339696, 1035065277647076057498170696375157234162477637697146392845283, 5205536456841339863165508421544725855479100318961870149291880], 'aut_phi_ratio': 15.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [2, 9, 2, 1], [2, 15, 2, 1], [2, 45, 1, 1], [2, 135, 2, 1], [2, 135, 4, 1], [2, 405, 1, 1], [2, 405, 2, 1], [3, 2, 1, 1], [3, 6, 2, 1], [3, 12, 1, 1], [3, 40, 2, 1], [3, 80, 2, 1], [3, 240, 4, 1], [3, 480, 2, 1], [4, 90, 1, 2], [4, 810, 1, 2], [4, 810, 2, 2], [5, 144, 1, 1], [6, 18, 1, 1], [6, 18, 2, 1], [6, 30, 2, 1], [6, 90, 1, 1], [6, 90, 4, 1], [6, 120, 2, 1], [6, 180, 2, 1], [6, 240, 2, 1], [6, 270, 2, 2], [6, 270, 4, 1], [6, 360, 2, 1], [6, 360, 4, 1], [6, 540, 1, 1], [6, 720, 2, 1], [6, 720, 4, 2], [6, 810, 1, 1], [6, 810, 2, 1], [6, 1080, 2, 1], [6, 1080, 4, 1], [6, 1440, 2, 1], [6, 2160, 2, 1], [6, 2160, 4, 1], [10, 1296, 1, 1], [10, 1296, 2, 1], [12, 180, 1, 2], [12, 540, 2, 2], [12, 1080, 1, 2], [12, 1620, 1, 2], [12, 1620, 2, 2], [15, 288, 1, 1], [15, 864, 2, 1], [15, 1728, 1, 1], [30, 2592, 1, 1], [30, 2592, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3.S_3\\wr C_2.A_6.C_2^2', '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': None, 'autcentquo_hash': 4510848913879562672, 'autcentquo_nilpotent': False, 'autcentquo_order': 311040, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3.S_3\\wr C_2.A_6.C_2^2', 'cc_stats': [[1, 1, 1], [2, 9, 3], [2, 15, 2], [2, 45, 1], [2, 135, 6], [2, 405, 3], [3, 2, 1], [3, 6, 2], [3, 12, 1], [3, 40, 2], [3, 80, 2], [3, 240, 4], [3, 480, 2], [4, 90, 2], [4, 810, 6], [5, 144, 1], [6, 18, 3], [6, 30, 2], [6, 90, 5], [6, 120, 2], [6, 180, 2], [6, 240, 2], [6, 270, 8], [6, 360, 6], [6, 540, 1], [6, 720, 10], [6, 810, 3], [6, 1080, 6], [6, 1440, 2], [6, 2160, 6], [10, 1296, 3], [12, 180, 2], [12, 540, 4], [12, 1080, 2], [12, 1620, 6], [15, 288, 1], [15, 864, 2], [15, 1728, 1], [30, 2592, 3]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '77760.bo', 'commutator_count': 1, 'commutator_label': '9720.bc', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '360.118'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 41, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['108.17', 1], ['720.763', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 3], [2, 15, 1, 2], [2, 45, 1, 1], [2, 135, 1, 6], [2, 405, 1, 3], [3, 2, 1, 1], [3, 6, 1, 2], [3, 12, 1, 1], [3, 40, 1, 2], [3, 80, 1, 2], [3, 240, 1, 4], [3, 480, 1, 2], [4, 90, 1, 2], [4, 810, 1, 6], [5, 144, 1, 1], [6, 18, 1, 3], [6, 30, 1, 2], [6, 90, 1, 5], [6, 120, 1, 2], [6, 180, 1, 2], [6, 240, 1, 2], [6, 270, 1, 8], [6, 360, 1, 6], [6, 540, 1, 1], [6, 720, 1, 10], [6, 810, 1, 3], [6, 1080, 1, 6], [6, 1440, 1, 2], [6, 2160, 1, 6], [10, 1296, 1, 3], [12, 180, 1, 2], [12, 540, 1, 4], [12, 1080, 1, 2], [12, 1620, 1, 6], [15, 288, 1, 1], [15, 864, 1, 2], [15, 1728, 1, 1], [30, 2592, 1, 3]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 364476672, 'exponent': 60, 'exponents_of_order': [6, 5, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[30, 1, 8], [54, 1, 4], [60, 1, 4], [96, 1, 2]], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '25920.w', 'hash': 4343203790838598385, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [6, 3, 2, 3, 2, 10, 3], 'inner_gens': [[138389, 224515, 3986397, 80644, 5309, 93924587997, 80880], [357834, 316920, 3812645, 45504, 40585, 93924414245, 45363], [357834, 179012, 3634559, 243, 40585, 93967781759, 45363], [219122, 362187, 3634559, 243, 85946, 93924236159, 80880], [218885, 281788, 3669692, 148, 85805, 93924271292, 45504], [357834, 179012, 442641029759, 243, 40585, 93924236159, 45363], [138389, 281788, 3669692, 243, 5309, 93924271292, 80880]], 'inner_hash': 4343203790838598385, 'inner_nilpotent': False, 'inner_order': 77760, 'inner_split': True, 'inner_tex': 'C_3^2:D_6\\times S_6', 'inner_used': [1, 2, 3, 5, 6], 'irrC_degree': 30, 'irrQ_degree': 30, 'irrQ_dim': 30, 'irrR_degree': 30, 'irrep_stats': [[1, 8], [2, 8], [4, 2], [5, 16], [6, 4], [9, 8], [10, 24], [16, 4], [18, 8], [20, 12], [30, 8], [32, 4], [36, 2], [40, 2], [54, 4], [60, 4], [64, 1], [96, 2]], 'label': '77760.bo', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C3^2:D6*S6', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 64, 'number_characteristic_subgroups': 17, 'number_conjugacy_classes': 121, 'number_divisions': 121, 'number_normal_subgroups': 41, 'number_subgroup_autclasses': 2849, 'number_subgroup_classes': 7808, 'number_subgroups': 2059265, 'old_label': None, 'order': 77760, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 2127], [3, 2186], [4, 5040], [5, 144], [6, 38454], [10, 3888], [12, 14400], [15, 3744], [30, 7776]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [0, 442680940800], 'outer_gens': [[138718, 80644, 3669385, 362187, 86155, 93924270985, 224515], [322413, 179012, 199348168892, 243, 85805, 193560232892, 45363]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': None, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 8], [4, 2], [5, 16], [6, 4], [9, 8], [10, 24], [16, 4], [18, 8], [20, 12], [30, 8], [32, 4], [36, 2], [40, 2], [54, 4], [60, 4], [64, 1], [96, 2]], 'representations': {'Perm': {'d': 15, 'gens': [138389, 316920, 3634559, 243, 85805, 93924236159, 80880]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^2:D_6\\times S_6', 'transitive_degree': 54, '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: 167269265
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 41, 'group_order': 77760, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 167269298
    {'aut_label': '2A', 'centralizer': '9.a1', 'counter': 2, 'group_counter': 41, 'group_order': 77760, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 5161, 'size': 9}
  • id: 167269309
    {'aut_label': '2B', 'centralizer': '9.b1', 'counter': 3, 'group_counter': 41, 'group_order': 77760, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 450, 'size': 9}
  • id: 167269320
    {'aut_label': '2A', 'centralizer': '9.a1', 'counter': 4, 'group_counter': 41, 'group_order': 77760, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 5759, 'size': 9}
  • id: 167269331
    {'aut_label': '2D', 'centralizer': '15.a1', 'counter': 5, 'group_counter': 41, 'group_order': 77760, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 3628800, 'size': 15}
  • id: 167269342
    {'aut_label': '2D', 'centralizer': '15.a1', 'counter': 6, 'group_counter': 41, 'group_order': 77760, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 87660921600, 'size': 15}
  • id: 167269353
    {'aut_label': '2F', 'centralizer': '45.b1', 'counter': 7, 'group_counter': 41, 'group_order': 77760, 'label': '2F', 'order': 2, 'powers': [1, 7, 7], 'representative': 1037836800, 'size': 45}
  • id: 167269364
    {'aut_label': '2G', 'centralizer': '135.a1', 'counter': 8, 'group_counter': 41, 'group_order': 77760, 'label': '2G', 'order': 2, 'powers': [1, 8, 8], 'representative': 3634559, 'size': 135}
  • id: 167269375
    {'aut_label': '2H', 'centralizer': '135.b1', 'counter': 9, 'group_counter': 41, 'group_order': 77760, 'label': '2H', 'order': 2, 'powers': [1, 9, 9], 'representative': 3629398, 'size': 135}
  • id: 167269266
    {'aut_label': '2G', 'centralizer': '135.a1', 'counter': 10, 'group_counter': 41, 'group_order': 77760, 'label': '2I', 'order': 2, 'powers': [1, 10, 10], 'representative': 3714746, 'size': 135}
  • id: 167269277
    {'aut_label': '2G', 'centralizer': '135.a1', 'counter': 11, 'group_counter': 41, 'group_order': 77760, 'label': '2J', 'order': 2, 'powers': [1, 11, 11], 'representative': 87660927359, 'size': 135}
  • id: 167269288
    {'aut_label': '2H', 'centralizer': '135.b1', 'counter': 12, 'group_counter': 41, 'group_order': 77760, 'label': '2K', 'order': 2, 'powers': [1, 12, 12], 'representative': 87660922198, 'size': 135}
  • id: 167269291
    {'aut_label': '2G', 'centralizer': '135.a1', 'counter': 13, 'group_counter': 41, 'group_order': 77760, 'label': '2L', 'order': 2, 'powers': [1, 13, 13], 'representative': 87661007546, 'size': 135}
  • id: 167269292
    {'aut_label': '2M', 'centralizer': '405.b1', 'counter': 14, 'group_counter': 41, 'group_order': 77760, 'label': '2M', 'order': 2, 'powers': [1, 14, 14], 'representative': 87261758909, 'size': 405}
  • id: 167269293
    {'aut_label': '2N', 'centralizer': '405.c1', 'counter': 15, 'group_counter': 41, 'group_order': 77760, 'label': '2N', 'order': 2, 'powers': [1, 15, 15], 'representative': 180623801971, 'size': 405}
  • id: 167269294
    {'aut_label': '2M', 'centralizer': '405.b1', 'counter': 16, 'group_counter': 41, 'group_order': 77760, 'label': '2O', 'order': 2, 'powers': [1, 16, 16], 'representative': 443639221050, 'size': 405}
  • id: 167269295
    {'aut_label': '3A', 'centralizer': '2.d1', 'counter': 17, 'group_counter': 41, 'group_order': 77760, 'label': '3A', 'order': 3, 'powers': [17, 1, 17], 'representative': 80787, 'size': 2}
  • id: 167269296
    {'aut_label': '3B', 'centralizer': '6.b1', 'counter': 18, 'group_counter': 41, 'group_order': 77760, 'label': '3B', 'order': 3, 'powers': [18, 1, 18], 'representative': 243, 'size': 6}
  • id: 167269297
    {'aut_label': '3B', 'centralizer': '6.b1', 'counter': 19, 'group_counter': 41, 'group_order': 77760, 'label': '3C', 'order': 3, 'powers': [19, 1, 19], 'representative': 362187, 'size': 6}
  • id: 167269299
    {'aut_label': '3D', 'centralizer': '12.l1', 'counter': 20, 'group_counter': 41, 'group_order': 77760, 'label': '3D', 'order': 3, 'powers': [20, 1, 20], 'representative': 281544, 'size': 12}
  • id: 167269300
    {'aut_label': '3E', 'centralizer': '40.f1', 'counter': 21, 'group_counter': 41, 'group_order': 77760, 'label': '3E', 'order': 3, 'powers': [21, 1, 21], 'representative': 79833600, 'size': 40}
  • id: 167269301
    {'aut_label': '3E', 'centralizer': '40.f1', 'counter': 22, 'group_counter': 41, 'group_order': 77760, 'label': '3F', 'order': 3, 'powers': [22, 1, 22], 'representative': 187848460800, 'size': 40}
  • id: 167269302
    {'aut_label': '3G', 'centralizer': '80.f1', 'counter': 23, 'group_counter': 41, 'group_order': 77760, 'label': '3G', 'order': 3, 'powers': [23, 1, 23], 'representative': 79914387, 'size': 80}
  • id: 167269303
    {'aut_label': '3G', 'centralizer': '80.f1', 'counter': 24, 'group_counter': 41, 'group_order': 77760, 'label': '3H', 'order': 3, 'powers': [24, 1, 24], 'representative': 187848541587, 'size': 80}
  • id: 167269304
    {'aut_label': '3I', 'centralizer': '240.a1', 'counter': 25, 'group_counter': 41, 'group_order': 77760, 'label': '3I', 'order': 3, 'powers': [25, 1, 25], 'representative': 187848460948, 'size': 240}
  • id: 167269305
    {'aut_label': '3I', 'centralizer': '240.a1', 'counter': 26, 'group_counter': 41, 'group_order': 77760, 'label': '3J', 'order': 3, 'powers': [26, 1, 26], 'representative': 93449082115, 'size': 240}
  • id: 167269306
    {'aut_label': '3I', 'centralizer': '240.a1', 'counter': 27, 'group_counter': 41, 'group_order': 77760, 'label': '3K', 'order': 3, 'powers': [27, 1, 27], 'representative': 93405536515, 'size': 240}
  • id: 167269307
    {'aut_label': '3I', 'centralizer': '240.a1', 'counter': 28, 'group_counter': 41, 'group_order': 77760, 'label': '3L', 'order': 3, 'powers': [28, 1, 28], 'representative': 43545748, 'size': 240}
  • id: 167269308
    {'aut_label': '3M', 'centralizer': '480.m1', 'counter': 29, 'group_counter': 41, 'group_order': 77760, 'label': '3M', 'order': 3, 'powers': [29, 1, 29], 'representative': 93485289331, 'size': 480}
  • id: 167269310
    {'aut_label': '3M', 'centralizer': '480.m1', 'counter': 30, 'group_counter': 41, 'group_order': 77760, 'label': '3N', 'order': 3, 'powers': [30, 1, 30], 'representative': 355419549624, 'size': 480}
  • id: 167269311
    {'aut_label': '4A', 'centralizer': '90.u1', 'counter': 31, 'group_counter': 41, 'group_order': 77760, 'label': '4A', 'order': 4, 'powers': [7, 31, 31], 'representative': 1437004800, 'size': 90}
  • id: 167269312
    {'aut_label': '4B', 'centralizer': '90.u1', 'counter': 32, 'group_counter': 41, 'group_order': 77760, 'label': '4B', 'order': 4, 'powers': [7, 32, 32], 'representative': 88615296000, 'size': 90}
  • id: 167269313
    {'aut_label': '4C', 'centralizer': '810.bf1', 'counter': 33, 'group_counter': 41, 'group_order': 77760, 'label': '4C', 'order': 4, 'powers': [7, 33, 33], 'representative': 368831549252, 'size': 810}
  • id: 167269314
    {'aut_label': '4D', 'centralizer': '810.ba1', 'counter': 34, 'group_counter': 41, 'group_order': 77760, 'label': '4D', 'order': 4, 'powers': [7, 34, 34], 'representative': 456013237946, 'size': 810}
  • id: 167269315
    {'aut_label': '4E', 'centralizer': '810.ba1', 'counter': 35, 'group_counter': 41, 'group_order': 77760, 'label': '4E', 'order': 4, 'powers': [7, 35, 35], 'representative': 26425279197, 'size': 810}
  • id: 167269316
    {'aut_label': '4F', 'centralizer': '810.bf1', 'counter': 36, 'group_counter': 41, 'group_order': 77760, 'label': '4F', 'order': 4, 'powers': [7, 36, 36], 'representative': 19639066293, 'size': 810}
  • id: 167269317
    {'aut_label': '4E', 'centralizer': '810.ba1', 'counter': 37, 'group_counter': 41, 'group_order': 77760, 'label': '4G', 'order': 4, 'powers': [7, 37, 37], 'representative': 174835624442, 'size': 810}
  • id: 167269318
    {'aut_label': '4D', 'centralizer': '810.ba1', 'counter': 38, 'group_counter': 41, 'group_order': 77760, 'label': '4H', 'order': 4, 'powers': [7, 38, 38], 'representative': 462236866558, 'size': 810}
  • id: 167269319
    {'aut_label': '5A', 'centralizer': '144.c1', 'counter': 39, 'group_counter': 41, 'group_order': 77760, 'label': '5A', 'order': 5, 'powers': [39, 39, 1], 'representative': 187768627200, 'size': 144}
  • id: 167269321
    {'aut_label': '6A', 'centralizer': '18.a1', 'counter': 40, 'group_counter': 41, 'group_order': 77760, 'label': '6A', 'order': 6, 'powers': [19, 2, 40], 'representative': 276629, 'size': 18}
  • id: 167269322
    {'aut_label': '6B', 'centralizer': '18.j1', 'counter': 41, 'group_counter': 41, 'group_order': 77760, 'label': '6B', 'order': 6, 'powers': [17, 3, 41], 'representative': 46054, 'size': 18}
  • id: 167269323
    {'aut_label': '6A', 'centralizer': '18.a1', 'counter': 42, 'group_counter': 41, 'group_order': 77760, 'label': '6C', 'order': 6, 'powers': [18, 4, 42], 'representative': 5516, 'size': 18}
  • id: 167269324
    {'aut_label': '6D', 'centralizer': '30.k1', 'counter': 43, 'group_counter': 41, 'group_order': 77760, 'label': '6D', 'order': 6, 'powers': [17, 5, 43], 'representative': 3674404, 'size': 30}
  • id: 167269325
    {'aut_label': '6D', 'centralizer': '30.k1', 'counter': 44, 'group_counter': 41, 'group_order': 77760, 'label': '6E', 'order': 6, 'powers': [17, 6, 44], 'representative': 87660967204, 'size': 30}
  • id: 167269326
    {'aut_label': '6F', 'centralizer': '90.c1', 'counter': 45, 'group_counter': 41, 'group_order': 77760, 'label': '6F', 'order': 6, 'powers': [18, 5, 45], 'representative': 3628948, 'size': 90}
  • id: 167269327
    {'aut_label': '6F', 'centralizer': '90.c1', 'counter': 46, 'group_counter': 41, 'group_order': 77760, 'label': '6G', 'order': 6, 'powers': [19, 5, 46], 'representative': 3772775, 'size': 90}
  • id: 167269328
    {'aut_label': '6F', 'centralizer': '90.c1', 'counter': 47, 'group_counter': 41, 'group_order': 77760, 'label': '6H', 'order': 6, 'powers': [18, 6, 47], 'representative': 87660921748, 'size': 90}
  • id: 167269329
    {'aut_label': '6F', 'centralizer': '90.c1', 'counter': 48, 'group_counter': 41, 'group_order': 77760, 'label': '6I', 'order': 6, 'powers': [19, 6, 48], 'representative': 87661065575, 'size': 90}
  • id: 167269330
    {'aut_label': '6J', 'centralizer': '90.bi1', 'counter': 49, 'group_counter': 41, 'group_order': 77760, 'label': '6J', 'order': 6, 'powers': [17, 7, 49], 'representative': 1037917587, 'size': 90}
  • id: 167269332
    {'aut_label': '6K', 'centralizer': '120.s1', 'counter': 50, 'group_counter': 41, 'group_order': 77760, 'label': '6K', 'order': 6, 'powers': [21, 5, 50], 'representative': 6270566400, 'size': 120}
  • id: 167269333
    {'aut_label': '6K', 'centralizer': '120.s1', 'counter': 51, 'group_counter': 41, 'group_order': 77760, 'label': '6L', 'order': 6, 'powers': [22, 6, 51], 'representative': 93927859200, 'size': 120}
  • id: 167269334
    {'aut_label': '6M', 'centralizer': '180.ef1', 'counter': 52, 'group_counter': 41, 'group_order': 77760, 'label': '6M', 'order': 6, 'powers': [20, 5, 52], 'representative': 3772531, 'size': 180}
  • id: 167269335
    {'aut_label': '6M', 'centralizer': '180.ef1', 'counter': 53, 'group_counter': 41, 'group_order': 77760, 'label': '6N', 'order': 6, 'powers': [20, 6, 53], 'representative': 87661065331, 'size': 180}
  • id: 167269336
    {'aut_label': '6O', 'centralizer': '240.z1', 'counter': 54, 'group_counter': 41, 'group_order': 77760, 'label': '6O', 'order': 6, 'powers': [23, 5, 54], 'representative': 6270612004, 'size': 240}
  • id: 167269337
    {'aut_label': '6O', 'centralizer': '240.z1', 'counter': 55, 'group_counter': 41, 'group_order': 77760, 'label': '6P', 'order': 6, 'powers': [24, 6, 55], 'representative': 93927904804, 'size': 240}
  • id: 167269338
    {'aut_label': '6Q', 'centralizer': '270.c1', 'counter': 56, 'group_counter': 41, 'group_order': 77760, 'label': '6Q', 'order': 6, 'powers': [18, 8, 56], 'representative': 3634316, 'size': 270}
  • id: 167269339
    {'aut_label': '6R', 'centralizer': '270.bn1', 'counter': 57, 'group_counter': 41, 'group_order': 77760, 'label': '6R', 'order': 6, 'powers': [17, 9, 57], 'representative': 3674613, 'size': 270}
  • id: 167269340
    {'aut_label': '6Q', 'centralizer': '270.c1', 'counter': 58, 'group_counter': 41, 'group_order': 77760, 'label': '6S', 'order': 6, 'powers': [19, 10, 58], 'representative': 3767518, 'size': 270}
  • id: 167269341
    {'aut_label': '6Q', 'centralizer': '270.c1', 'counter': 59, 'group_counter': 41, 'group_order': 77760, 'label': '6T', 'order': 6, 'powers': [18, 11, 59], 'representative': 87660927116, 'size': 270}
  • id: 167269343
    {'aut_label': '6R', 'centralizer': '270.bn1', 'counter': 60, 'group_counter': 41, 'group_order': 77760, 'label': '6U', 'order': 6, 'powers': [17, 12, 60], 'representative': 87660967413, 'size': 270}
  • id: 167269344
    {'aut_label': '6Q', 'centralizer': '270.c1', 'counter': 61, 'group_counter': 41, 'group_order': 77760, 'label': '6V', 'order': 6, 'powers': [19, 13, 61], 'representative': 87661060318, 'size': 270}
  • id: 167269345
    {'aut_label': '6W', 'centralizer': '270.o1', 'counter': 62, 'group_counter': 41, 'group_order': 77760, 'label': '6W', 'order': 6, 'powers': [19, 7, 62], 'representative': 87262035388, 'size': 270}
  • id: 167269346
    {'aut_label': '6W', 'centralizer': '270.o1', 'counter': 63, 'group_counter': 41, 'group_order': 77760, 'label': '6X', 'order': 6, 'powers': [18, 7, 63], 'representative': 87261753843, 'size': 270}
  • id: 167269347
    {'aut_label': '6Y', 'centralizer': '360.v1', 'counter': 64, 'group_counter': 41, 'group_order': 77760, 'label': '6Y', 'order': 6, 'powers': [21, 4, 64], 'representative': 442162108555, 'size': 360}
  • id: 167269348
    {'aut_label': '6Z', 'centralizer': '360.x1', 'counter': 65, 'group_counter': 41, 'group_order': 77760, 'label': '6Z', 'order': 6, 'powers': [21, 3, 65], 'representative': 354980102850, 'size': 360}
  • id: 167269349
    {'aut_label': '6Y', 'centralizer': '360.v1', 'counter': 66, 'group_counter': 41, 'group_order': 77760, 'label': '6AA', 'order': 6, 'powers': [22, 4, 66], 'representative': 455091655825, 'size': 360}
  • id: 167269350
    {'aut_label': '6Y', 'centralizer': '360.v1', 'counter': 67, 'group_counter': 41, 'group_order': 77760, 'label': '6AB', 'order': 6, 'powers': [21, 2, 67], 'representative': 262013915642, 'size': 360}
  • id: 167269351
    {'aut_label': '6Y', 'centralizer': '360.v1', 'counter': 68, 'group_counter': 41, 'group_order': 77760, 'label': '6AC', 'order': 6, 'powers': [22, 2, 68], 'representative': 449782542985, 'size': 360}
  • id: 167269352
    {'aut_label': '6Z', 'centralizer': '360.x1', 'counter': 69, 'group_counter': 41, 'group_order': 77760, 'label': '6AD', 'order': 6, 'powers': [22, 3, 69], 'representative': 107336499384, 'size': 360}
  • id: 167269354
    {'aut_label': '6AE', 'centralizer': '540.fz1', 'counter': 70, 'group_counter': 41, 'group_order': 77760, 'label': '6AE', 'order': 6, 'powers': [20, 7, 70], 'representative': 87261932851, 'size': 540}
  • id: 167269355
    {'aut_label': '6AF', 'centralizer': '720.b1', 'counter': 71, 'group_counter': 41, 'group_order': 77760, 'label': '6AF', 'order': 6, 'powers': [27, 2, 71], 'representative': 174356939762, 'size': 720}
  • id: 167269356
    {'aut_label': '6AG', 'centralizer': '720.f1', 'counter': 72, 'group_counter': 41, 'group_order': 77760, 'label': '6AG', 'order': 6, 'powers': [28, 5, 72], 'representative': 87258125043, 'size': 720}
  • id: 167269357
    {'aut_label': '6AG', 'centralizer': '720.f1', 'counter': 73, 'group_counter': 41, 'group_order': 77760, 'label': '6AH', 'order': 6, 'powers': [27, 5, 73], 'representative': 186894265412, 'size': 720}
  • id: 167269358
    {'aut_label': '6AF', 'centralizer': '720.b1', 'counter': 74, 'group_counter': 41, 'group_order': 77760, 'label': '6AI', 'order': 6, 'powers': [25, 4, 74], 'representative': 350190091916, 'size': 720}
  • id: 167269359
    {'aut_label': '6AJ', 'centralizer': '720.bm1', 'counter': 75, 'group_counter': 41, 'group_order': 77760, 'label': '6AJ', 'order': 6, 'powers': [24, 3, 75], 'representative': 106897507891, 'size': 720}
  • id: 167269360
    {'aut_label': '6AG', 'centralizer': '720.f1', 'counter': 76, 'group_counter': 41, 'group_order': 77760, 'label': '6AK', 'order': 6, 'powers': [26, 6, 76], 'representative': 107340220920, 'size': 720}
  • id: 167269361
    {'aut_label': '6AF', 'centralizer': '720.b1', 'counter': 77, 'group_counter': 41, 'group_order': 77760, 'label': '6AL', 'order': 6, 'powers': [26, 2, 77], 'representative': 461278817282, 'size': 720}
  • id: 167269362
    {'aut_label': '6AG', 'centralizer': '720.f1', 'counter': 78, 'group_counter': 41, 'group_order': 77760, 'label': '6AM', 'order': 6, 'powers': [25, 6, 78], 'representative': 456089437680, 'size': 720}
  • id: 167269363
    {'aut_label': '6AJ', 'centralizer': '720.bm1', 'counter': 79, 'group_counter': 41, 'group_order': 77760, 'label': '6AN', 'order': 6, 'powers': [23, 3, 79], 'representative': 13016684427, 'size': 720}
  • id: 167269365
    {'aut_label': '6AF', 'centralizer': '720.b1', 'counter': 80, 'group_counter': 41, 'group_order': 77760, 'label': '6AO', 'order': 6, 'powers': [28, 4, 80], 'representative': 43764485, 'size': 720}
  • id: 167269366
    {'aut_label': '6AP', 'centralizer': '810.h1', 'counter': 81, 'group_counter': 41, 'group_order': 77760, 'label': '6AP', 'order': 6, 'powers': [19, 14, 81], 'representative': 87261937918, 'size': 810}
  • id: 167269367
    {'aut_label': '6AQ', 'centralizer': '810.br1', 'counter': 82, 'group_counter': 41, 'group_order': 77760, 'label': '6AQ', 'order': 6, 'powers': [17, 15, 82], 'representative': 180623882852, 'size': 810}
  • id: 167269368
    {'aut_label': '6AP', 'centralizer': '810.h1', 'counter': 83, 'group_counter': 41, 'group_order': 77760, 'label': '6AR', 'order': 6, 'powers': [18, 16, 83], 'representative': 443639301694, 'size': 810}
  • id: 167269369
    {'aut_label': '6AS', 'centralizer': '1080.bl1', 'counter': 84, 'group_counter': 41, 'group_order': 77760, 'label': '6AS', 'order': 6, 'powers': [22, 12, 84], 'representative': 93928083384, 'size': 1080}
  • id: 167269370
    {'aut_label': '6AT', 'centralizer': '1080.bi1', 'counter': 85, 'group_counter': 41, 'group_order': 77760, 'label': '6AT', 'order': 6, 'powers': [22, 11, 85], 'representative': 281696492159, 'size': 1080}
  • id: 167269371
    {'aut_label': '6AT', 'centralizer': '1080.bi1', 'counter': 86, 'group_counter': 41, 'group_order': 77760, 'label': '6AU', 'order': 6, 'powers': [22, 13, 86], 'representative': 93927945005, 'size': 1080}
  • id: 167269372
    {'aut_label': '6AT', 'centralizer': '1080.bi1', 'counter': 87, 'group_counter': 41, 'group_order': 77760, 'label': '6AV', 'order': 6, 'powers': [21, 10, 87], 'representative': 87258210505, 'size': 1080}
  • id: 167269373
    {'aut_label': '6AS', 'centralizer': '1080.bl1', 'counter': 88, 'group_counter': 41, 'group_order': 77760, 'label': '6AW', 'order': 6, 'powers': [21, 9, 88], 'representative': 93445229250, 'size': 1080}
  • id: 167269374
    {'aut_label': '6AT', 'centralizer': '1080.bi1', 'counter': 89, 'group_counter': 41, 'group_order': 77760, 'label': '6AX', 'order': 6, 'powers': [21, 8, 89], 'representative': 107376549597, 'size': 1080}
  • id: 167269376
    {'aut_label': '6AY', 'centralizer': '1440.t1', 'counter': 90, 'group_counter': 41, 'group_order': 77760, 'label': '6AY', 'order': 6, 'powers': [29, 6, 90], 'representative': 287920159944, 'size': 1440}
  • id: 167269377
    {'aut_label': '6AY', 'centralizer': '1440.t1', 'counter': 91, 'group_counter': 41, 'group_order': 77760, 'label': '6AZ', 'order': 6, 'powers': [30, 5, 91], 'representative': 287481017975, 'size': 1440}
  • id: 167269378
    {'aut_label': '6BA', 'centralizer': '2160.bo1', 'counter': 92, 'group_counter': 41, 'group_order': 77760, 'label': '6BA', 'order': 6, 'powers': [24, 12, 92], 'representative': 281696567730, 'size': 2160}
  • id: 167269379
    {'aut_label': '6BB', 'centralizer': '2160.a1', 'counter': 93, 'group_counter': 41, 'group_order': 77760, 'label': '6BB', 'order': 6, 'powers': [25, 11, 93], 'representative': 93927864716, 'size': 2160}
  • id: 167269380
    {'aut_label': '6BB', 'centralizer': '2160.a1', 'counter': 94, 'group_counter': 41, 'group_order': 77760, 'label': '6BC', 'order': 6, 'powers': [26, 13, 94], 'representative': 281696763029, 'size': 2160}
  • id: 167269381
    {'aut_label': '6BB', 'centralizer': '2160.a1', 'counter': 95, 'group_counter': 41, 'group_order': 77760, 'label': '6BD', 'order': 6, 'powers': [28, 8, 95], 'representative': 26345410314, 'size': 2160}
  • id: 167269382
    {'aut_label': '6BB', 'centralizer': '2160.a1', 'counter': 96, 'group_counter': 41, 'group_order': 77760, 'label': '6BE', 'order': 6, 'powers': [27, 10, 96], 'representative': 93409079610, 'size': 2160}
  • id: 167269383
    {'aut_label': '6BA', 'centralizer': '2160.bo1', 'counter': 97, 'group_counter': 41, 'group_order': 77760, 'label': '6BF', 'order': 6, 'powers': [23, 9, 97], 'representative': 19682835244, 'size': 2160}
  • id: 167269384
    {'aut_label': '10A', 'centralizer': '1296.g1', 'counter': 98, 'group_counter': 41, 'group_order': 77760, 'label': '10A', 'order': 10, 'powers': [39, 98, 2], 'representative': 93924235561, 'size': 1296}
  • id: 167269385
    {'aut_label': '10B', 'centralizer': '1296.h1', 'counter': 99, 'group_counter': 41, 'group_order': 77760, 'label': '10B', 'order': 10, 'powers': [39, 99, 3], 'representative': 373701082050, 'size': 1296}
  • id: 167269267
    {'aut_label': '10A', 'centralizer': '1296.g1', 'counter': 100, 'group_counter': 41, 'group_order': 77760, 'label': '10C', 'order': 10, 'powers': [39, 100, 4], 'representative': 281253778559, 'size': 1296}
  • id: 167269268
    {'aut_label': '12A', 'centralizer': '180.cs1', 'counter': 101, 'group_counter': 41, 'group_order': 77760, 'label': '12A', 'order': 12, 'powers': [49, 31, 101], 'representative': 522592804, 'size': 180}
  • id: 167269269
    {'aut_label': '12B', 'centralizer': '180.cs1', 'counter': 102, 'group_counter': 41, 'group_order': 77760, 'label': '12B', 'order': 12, 'powers': [49, 32, 102], 'representative': 87700884004, 'size': 180}
  • id: 167269270
    {'aut_label': '12C', 'centralizer': '540.l1', 'counter': 103, 'group_counter': 41, 'group_order': 77760, 'label': '12C', 'order': 12, 'powers': [63, 32, 103], 'representative': 287923507348, 'size': 540}
  • id: 167269271
    {'aut_label': '12D', 'centralizer': '540.l1', 'counter': 104, 'group_counter': 41, 'group_order': 77760, 'label': '12D', 'order': 12, 'powers': [62, 31, 104], 'representative': 287444649575, 'size': 540}
  • id: 167269272
    {'aut_label': '12D', 'centralizer': '540.l1', 'counter': 105, 'group_counter': 41, 'group_order': 77760, 'label': '12E', 'order': 12, 'powers': [63, 31, 105], 'representative': 287444550963, 'size': 540}
  • id: 167269273
    {'aut_label': '12C', 'centralizer': '540.l1', 'counter': 106, 'group_counter': 41, 'group_order': 77760, 'label': '12F', 'order': 12, 'powers': [62, 32, 106], 'representative': 448824816120, 'size': 540}
  • id: 167269274
    {'aut_label': '12G', 'centralizer': '1080.dy1', 'counter': 107, 'group_counter': 41, 'group_order': 77760, 'label': '12G', 'order': 12, 'powers': [70, 32, 107], 'representative': 456013433643, 'size': 1080}
  • id: 167269275
    {'aut_label': '12H', 'centralizer': '1080.dy1', 'counter': 108, 'group_counter': 41, 'group_order': 77760, 'label': '12H', 'order': 12, 'powers': [70, 31, 108], 'representative': 442597622131, 'size': 1080}
  • id: 167269276
    {'aut_label': '12I', 'centralizer': '1620.cv1', 'counter': 109, 'group_counter': 41, 'group_order': 77760, 'label': '12I', 'order': 12, 'powers': [49, 33, 109], 'representative': 281693220355, 'size': 1620}
  • id: 167269278
    {'aut_label': '12J', 'centralizer': '1620.a1', 'counter': 110, 'group_counter': 41, 'group_order': 77760, 'label': '12J', 'order': 12, 'powers': [62, 34, 110], 'representative': 287923645918, 'size': 1620}
  • id: 167269279
    {'aut_label': '12K', 'centralizer': '1620.a1', 'counter': 111, 'group_counter': 41, 'group_order': 77760, 'label': '12K', 'order': 12, 'powers': [63, 35, 111], 'representative': 20201806558, 'size': 1620}
  • id: 167269280
    {'aut_label': '12L', 'centralizer': '1620.cv1', 'counter': 112, 'group_counter': 41, 'group_order': 77760, 'label': '12L', 'order': 12, 'powers': [49, 36, 112], 'representative': 13452007554, 'size': 1620}
  • id: 167269281
    {'aut_label': '12K', 'centralizer': '1620.a1', 'counter': 113, 'group_counter': 41, 'group_order': 77760, 'label': '12M', 'order': 12, 'powers': [62, 37, 113], 'representative': 99632471610, 'size': 1620}
  • id: 167269282
    {'aut_label': '12J', 'centralizer': '1620.a1', 'counter': 114, 'group_counter': 41, 'group_order': 77760, 'label': '12N', 'order': 12, 'powers': [63, 38, 114], 'representative': 281736761034, 'size': 1620}
  • id: 167269283
    {'aut_label': '15A', 'centralizer': '288.b1', 'counter': 115, 'group_counter': 41, 'group_order': 77760, 'label': '15A', 'order': 15, 'powers': [115, 39, 17], 'representative': 194554528804, 'size': 288}
  • id: 167269284
    {'aut_label': '15B', 'centralizer': '864.a1', 'counter': 116, 'group_counter': 41, 'group_order': 77760, 'label': '15B', 'order': 15, 'powers': [116, 39, 19], 'representative': 348713446588, 'size': 864}
  • id: 167269285
    {'aut_label': '15B', 'centralizer': '864.a1', 'counter': 117, 'group_counter': 41, 'group_order': 77760, 'label': '15C', 'order': 15, 'powers': [117, 39, 18], 'representative': 374579251443, 'size': 864}
  • id: 167269286
    {'aut_label': '15D', 'centralizer': '1728.b1', 'counter': 118, 'group_counter': 41, 'group_order': 77760, 'label': '15D', 'order': 15, 'powers': [118, 39, 20], 'representative': 94363459076, 'size': 1728}
  • id: 167269287
    {'aut_label': '30A', 'centralizer': '2592.a1', 'counter': 119, 'group_counter': 41, 'group_order': 77760, 'label': '30A', 'order': 30, 'powers': [116, 98, 40], 'representative': 187768846794, 'size': 2592}
  • id: 167269289
    {'aut_label': '30B', 'centralizer': '2592.d1', 'counter': 120, 'group_counter': 41, 'group_order': 77760, 'label': '30B', 'order': 30, 'powers': [115, 99, 41], 'representative': 94406942037, 'size': 2592}
  • id: 167269290
    {'aut_label': '30A', 'centralizer': '2592.a1', 'counter': 121, 'group_counter': 41, 'group_order': 77760, 'label': '30C', 'order': 30, 'powers': [117, 100, 42], 'representative': 436370463211, 'size': 2592}
• 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: 16782222
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 16782255
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -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: 16782266
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, -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: 16782277
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 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: 16782288
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 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: 16782299
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -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: 16782310
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -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: 16782321
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 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: 16782332
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, -1, -1, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, -1, 0, 2, 2, -1, -1, 2, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, -1, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, -1, -1, 0, 2, 0, 0, -1, -1, 2, 0, -1, 0, -1, 0, 2, 2, 0, 0, 0, 0, -1, -1, 0, 0, -1, 0, -1, 0, 2, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, -1, 0, 0, 0, -1, 0, 2, -1, 2, -1, -1, 0, 0], 'schur_index': 1}
  • id: 16782223
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, -1, 2, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, 0, 2, 0, 2, 0, 0, 2, -1, 0, 0, 2, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, 2, 2, 0, 0, 2, 0, -1, -1, 0, -1, 0, 0, 2, 0, 2, 0, -1, 2, -1, -1, 0, -1, 2, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 2, -1, -1, -1, 0, 0, -1, 0, 0, 0, 0, 2, 2, 2, -1, -1, 2, 2, -1, -1, 0, -1, -1, 0, 0, 0, 2, 2, -1, -1, 0, 0, -1], 'schur_index': 1}
  • id: 16782234
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.2c', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, -2, -2, 2, 0, 0, 0, 2, 2, 0, 0, 0, -2, 2, -1, 2, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -2, 2, 0, 2, 0, -2, 0, 0, 2, 1, 0, 0, -2, -2, -2, -2, 2, 1, 1, -2, -2, 1, 1, -2, -2, 0, 0, 2, 0, -1, -1, 0, -1, 0, 0, -2, 0, -2, 0, -1, -2, 1, 1, 0, 1, -2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 1, 1, -1, 0, 0, -1, 0, 0, 0, 0, -2, -2, 2, -1, 1, 2, -2, -1, 1, 0, -1, 1, 0, 0, 0, 2, 2, -1, -1, 0, 0, 1], 'schur_index': 1}
  • id: 16782245
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 2, 2, 2, 0, 0, 0, -2, -2, 0, 0, 0, -2, 2, -1, 2, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, 0, -2, 0, -2, 0, 0, 2, 1, 0, 0, 2, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, 2, 2, 0, 0, 2, 0, 1, -1, 0, 1, 0, 0, -2, 0, -2, 0, -1, 2, 1, -1, 0, 1, 2, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, -2, -1, -1, 1, 0, 0, 1, 0, 0, 0, 0, -2, 2, 2, -1, -1, 2, 2, -1, -1, 0, 1, 1, 0, 0, 0, 2, 2, -1, -1, 0, 0, 1], 'schur_index': 1}
  • id: 16782248
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 0, -2, 0, -2, -2, 2, 0, 0, 2, 0, 0, 2, -2, 0, 0, 2, 2, -1, -1, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, -2, 2, 0, 0, 2, 0, -2, 0, 2, 0, 1, 0, -2, -2, 1, 1, 2, -2, -2, -2, -2, 1, 1, -2, -2, -1, -1, -1, 0, 0, 2, 0, 0, -2, -2, 0, 0, 0, 0, -1, 1, 0, -2, 0, 0, 1, 1, -2, 0, 1, 0, 1, 0, 2, 2, 0, 0, 0, 0, 1, 1, 0, 0, -1, 0, -1, 0, -2, 0, 0, -2, 2, 2, -2, -1, 1, -1, 1, -1, 0, 0, 0, 1, 0, 2, -1, 2, -1, 1, 0, 0], 'schur_index': 1}
  • id: 16782249
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 0, -2, 0, 2, 2, 2, 0, 0, -2, 0, 0, -2, -2, 0, 0, 2, 2, -1, -1, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, 2, 2, 0, 0, -2, 0, -2, 0, 2, 0, 1, 0, 2, 2, -1, -1, 2, 2, 2, 2, 2, -1, -1, 2, 2, 1, 1, -1, 0, 0, 2, 0, 0, -2, -2, 0, 0, 0, 0, -1, -1, 0, 2, 0, 0, -1, 1, 2, 0, 1, 0, 1, 0, -2, -2, 0, 0, 0, 0, -1, -1, 0, 0, 1, 0, 1, 0, -2, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, 1, 0, 0, 0, 1, 0, 2, -1, 2, -1, 1, 0, 0], 'schur_index': 1}
  • id: 16782250
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 0, 2, 0, -2, -2, 2, 0, 0, -2, 0, 0, -2, 2, 0, 0, 2, 2, -1, -1, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, -2, 2, 0, 0, -2, 0, 2, 0, 2, 0, -1, 0, -2, -2, 1, 1, 2, -2, -2, -2, -2, 1, 1, -2, -2, 1, 1, -1, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, -1, 1, 0, -2, 0, 0, 1, -1, -2, 0, -1, 0, -1, 0, -2, -2, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 2, 0, 0, -2, 2, 2, -2, -1, 1, -1, 1, 1, 0, 0, 0, -1, 0, 2, -1, 2, -1, -1, 0, 0], 'schur_index': 1}
  • id: 16782251
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 0, -2, -2, 2, 0, 0, 0, -2, -2, 0, 0, 0, 2, 2, -1, 2, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -2, 2, 0, -2, 0, 2, 0, 0, 2, -1, 0, 0, -2, -2, -2, -2, 2, 1, 1, -2, -2, 1, 1, -2, -2, 0, 0, 2, 0, 1, -1, 0, 1, 0, 0, 2, 0, 2, 0, -1, -2, -1, 1, 0, -1, -2, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, -2, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 2, -2, 2, -1, 1, 2, -2, -1, 1, 0, 1, -1, 0, 0, 0, 2, 2, -1, -1, 0, 0, -1], 'schur_index': 1}
  • id: 16782252
    {'cdim': 4, 'counter': 17, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.4a', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, 1, 4, 4, 4, 4, -2, -2, -2, -2, 1, 1, 4, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, -2, -2, 4, -2, -2, 4, 4, 1, 1, 4, 4, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, -2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -2, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 4, -2, -2, 1, 0, 0, 0], 'schur_index': 1}
  • id: 16782253
    {'cdim': 4, 'counter': 18, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.4b', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 0, 0, 0, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, 1, 4, 4, 4, 4, -2, -2, -2, -2, 1, 1, -4, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, -4, 2, 2, 4, 2, 2, -4, -4, -1, -1, -4, -4, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -2, 2, -2, 2, 1, -1, 0, 0, 0, 0, 0, 0, 4, -2, -2, 1, 0, 0, 0], 'schur_index': 1}
  • id: 16782254
    {'cdim': 5, 'counter': 19, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.5a', 'multiplicity': 1, 'nt': [6, 16], 'qdim': 5, 'qvalues': [5, 5, 5, 5, -1, 3, 1, -1, 3, -1, 3, -1, 3, 1, 1, 1, 5, 5, 5, 5, -1, 2, -1, 2, 2, -1, 2, -1, 2, -1, 1, -1, 1, 1, 1, -1, -1, -1, 0, 5, 5, 5, -1, 3, 3, -1, 1, -1, 3, -1, 0, -1, 3, -1, 0, -1, 3, 1, -1, -1, 1, 3, 3, 2, -1, -1, 2, 2, -1, 1, -1, 2, 0, -1, -1, 0, -1, -1, 2, 2, 1, 1, 1, 0, -1, 0, 0, -1, -1, 0, -1, 0, 0, -1, -1, 0, -1, 0, 0, 0, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782256
    {'cdim': 5, 'counter': 20, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.5b', 'multiplicity': 1, 'nt': [6, 16], 'qdim': 5, 'qvalues': [5, 5, 5, 5, 3, -1, 1, 3, -1, 3, -1, 3, -1, 1, 1, 1, 5, 5, 5, 5, 2, -1, 2, -1, -1, 2, -1, 2, -1, 2, 1, -1, 1, 1, 1, -1, -1, -1, 0, 5, 5, 5, 3, -1, -1, 3, 1, 3, -1, 0, -1, 3, -1, 0, -1, 3, -1, 1, 3, 3, 1, -1, -1, -1, 2, 2, -1, -1, 2, 1, 0, -1, -1, 2, 2, -1, 2, 0, -1, -1, 1, 1, 1, -1, 0, -1, -1, 0, 0, -1, 0, -1, -1, 0, 0, -1, 0, 0, 0, 0, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782257
    {'cdim': 5, 'counter': 21, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.5c', 'multiplicity': 1, 'nt': [12, 183], 'qdim': 5, 'qvalues': [5, 5, 5, 5, -3, 1, 1, -3, 1, -3, 1, -3, 1, 1, 1, 1, 5, 5, 5, 5, 2, -1, 2, -1, -1, 2, -1, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 0, 5, 5, 5, -3, 1, 1, -3, 1, -3, 1, 0, 1, -3, 1, 0, 1, -3, 1, 1, -3, -3, 1, 1, 1, -1, 2, 2, -1, -1, 2, 1, 0, -1, 1, 2, 2, 1, 2, 0, -1, -1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782258
    {'cdim': 5, 'counter': 22, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.5d', 'multiplicity': 1, 'nt': [12, 183], 'qdim': 5, 'qvalues': [5, 5, 5, 5, 1, -3, 1, 1, -3, 1, -3, 1, -3, 1, 1, 1, 5, 5, 5, 5, -1, 2, -1, 2, 2, -1, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 5, 5, 5, 1, -3, -3, 1, 1, 1, -3, 1, 0, 1, -3, 1, 0, 1, -3, 1, 1, 1, 1, -3, -3, 2, -1, -1, 2, 2, -1, 1, 1, 2, 0, -1, -1, 0, -1, 1, 2, 2, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782259
    {'cdim': 5, 'counter': 23, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.5e', 'multiplicity': 1, 'nt': [12, 219], 'qdim': 5, 'qvalues': [5, -5, -5, 5, -3, 1, 1, -3, 1, 3, -1, 3, -1, -1, 1, -1, 5, 5, 5, 5, 2, -1, 2, -1, -1, 2, -1, 2, -1, 2, -1, -1, -1, 1, 1, 1, 1, -1, 0, -5, -5, 5, -3, 1, 1, -3, 1, -3, 1, 0, 1, -3, 1, 0, 1, 3, -1, 1, -3, 3, 1, 1, -1, 1, -2, -2, -1, 1, 2, 1, 0, 1, 1, 2, -2, 1, -2, 0, -1, 1, -1, -1, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, 0, 0, -1, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782260
    {'cdim': 5, 'counter': 24, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.5f', 'multiplicity': 1, 'nt': [12, 219], 'qdim': 5, 'qvalues': [5, -5, -5, 5, -1, 3, 1, -1, 3, 1, -3, 1, -3, -1, 1, -1, 5, 5, 5, 5, -1, 2, -1, 2, 2, -1, 2, -1, 2, -1, 1, -1, 1, -1, -1, 1, 1, -1, 0, -5, -5, 5, -1, 3, 3, -1, 1, -1, 3, -1, 0, -1, 3, -1, 0, 1, -3, 1, -1, 1, 1, 3, -3, -2, 1, 1, 2, -2, -1, 1, -1, -2, 0, -1, 1, 0, 1, -1, 2, -2, -1, -1, 1, 0, 1, 0, 0, -1, 1, 0, -1, 0, 0, 1, 1, 0, -1, 0, 0, 0, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782261
    {'cdim': 5, 'counter': 25, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.5g', 'multiplicity': 1, 'nt': [12, 219], 'qdim': 5, 'qvalues': [5, -5, -5, 5, 1, -3, 1, 1, -3, -1, 3, -1, 3, -1, 1, -1, 5, 5, 5, 5, -1, 2, -1, 2, 2, -1, 2, -1, 2, -1, -1, -1, -1, 1, 1, 1, 1, -1, 0, -5, -5, 5, 1, -3, -3, 1, 1, 1, -3, 1, 0, 1, -3, 1, 0, -1, 3, 1, 1, -1, 1, -3, 3, -2, 1, 1, 2, -2, -1, 1, 1, -2, 0, -1, 1, 0, 1, 1, 2, -2, -1, -1, 1, 0, -1, 0, 0, 1, -1, 0, 1, 0, 0, -1, -1, 0, 1, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782262
    {'cdim': 5, 'counter': 26, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.5h', 'multiplicity': 1, 'nt': [12, 219], 'qdim': 5, 'qvalues': [5, -5, -5, 5, 3, -1, 1, 3, -1, -3, 1, -3, 1, -1, 1, -1, 5, 5, 5, 5, 2, -1, 2, -1, -1, 2, -1, 2, -1, 2, 1, -1, 1, -1, -1, 1, 1, -1, 0, -5, -5, 5, 3, -1, -1, 3, 1, 3, -1, 0, -1, 3, -1, 0, -1, -3, 1, 1, 3, -3, 1, -1, 1, 1, -2, -2, -1, 1, 2, 1, 0, 1, -1, 2, -2, -1, -2, 0, -1, 1, -1, -1, 1, 1, 0, -1, 1, 0, 0, -1, 0, 1, -1, 0, 0, 1, 0, 0, 0, 0, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782263
    {'cdim': 5, 'counter': 27, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.5i', 'multiplicity': 1, 'nt': [12, 219], 'qdim': 5, 'qvalues': [5, -5, 5, -5, -3, 1, 1, 3, -1, -3, -1, 3, 1, 1, -1, -1, 5, 5, 5, 5, 2, -1, 2, -1, -1, 2, -1, 2, -1, 2, -1, -1, 1, 1, -1, 1, -1, 1, 0, -5, 5, -5, -3, 1, 1, -3, 1, -3, 1, 0, 1, -3, 1, 0, 1, -3, 1, 1, 3, 3, 1, -1, -1, -1, 2, -2, 1, 1, -2, 1, 0, 1, 1, -2, -2, 1, 2, 0, 1, -1, -1, 1, -1, 1, 0, -1, -1, 0, 0, 1, 0, -1, -1, 0, 0, 1, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782264
    {'cdim': 5, 'counter': 28, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.5j', 'multiplicity': 1, 'nt': [12, 219], 'qdim': 5, 'qvalues': [5, -5, 5, -5, -1, 3, 1, 1, -3, -1, -3, 1, 3, 1, -1, -1, 5, 5, 5, 5, -1, 2, -1, 2, 2, -1, 2, -1, 2, -1, 1, -1, -1, -1, 1, 1, -1, 1, 0, -5, 5, -5, -1, 3, 3, -1, 1, -1, 3, -1, 0, -1, 3, -1, 0, -1, 3, 1, 1, 1, 1, -3, -3, 2, -1, 1, -2, -2, 1, 1, -1, -2, 0, 1, 1, 0, -1, -1, -2, 2, -1, 1, -1, 0, -1, 0, 0, 1, 1, 0, -1, 0, 0, -1, 1, 0, 1, 0, 0, 0, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782265
    {'cdim': 5, 'counter': 29, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.5k', 'multiplicity': 1, 'nt': [12, 219], 'qdim': 5, 'qvalues': [5, -5, 5, -5, 1, -3, 1, -1, 3, 1, 3, -1, -3, 1, -1, -1, 5, 5, 5, 5, -1, 2, -1, 2, 2, -1, 2, -1, 2, -1, -1, -1, 1, 1, -1, 1, -1, 1, 0, -5, 5, -5, 1, -3, -3, 1, 1, 1, -3, 1, 0, 1, -3, 1, 0, 1, -3, 1, -1, -1, 1, 3, 3, 2, -1, 1, -2, -2, 1, 1, 1, -2, 0, 1, 1, 0, -1, 1, -2, 2, -1, 1, -1, 0, 1, 0, 0, -1, -1, 0, 1, 0, 0, 1, -1, 0, -1, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782267
    {'cdim': 5, 'counter': 30, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.5l', 'multiplicity': 1, 'nt': [12, 219], 'qdim': 5, 'qvalues': [5, -5, 5, -5, 3, -1, 1, -3, 1, 3, 1, -3, -1, 1, -1, -1, 5, 5, 5, 5, 2, -1, 2, -1, -1, 2, -1, 2, -1, 2, 1, -1, -1, -1, 1, 1, -1, 1, 0, -5, 5, -5, 3, -1, -1, 3, 1, 3, -1, 0, -1, 3, -1, 0, -1, 3, -1, 1, -3, -3, 1, 1, 1, -1, 2, -2, 1, 1, -2, 1, 0, 1, -1, -2, -2, -1, 2, 0, 1, -1, -1, 1, -1, -1, 0, 1, 1, 0, 0, -1, 0, 1, 1, 0, 0, -1, 0, 0, 0, 0, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782268
    {'cdim': 5, 'counter': 31, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.5m', 'multiplicity': 1, 'nt': [12, 219], 'qdim': 5, 'qvalues': [5, 5, -5, -5, -3, 1, 1, 3, -1, 3, 1, -3, -1, -1, -1, 1, 5, 5, 5, 5, 2, -1, 2, -1, -1, 2, -1, 2, -1, 2, -1, -1, 1, -1, 1, -1, 1, 1, 0, 5, -5, -5, -3, 1, 1, -3, 1, -3, 1, 0, 1, -3, 1, 0, 1, 3, -1, 1, 3, -3, 1, -1, 1, 1, -2, 2, 1, -1, -2, 1, 0, -1, 1, -2, 2, 1, -2, 0, 1, 1, 1, -1, -1, -1, 0, -1, 1, 0, 0, 1, 0, 1, -1, 0, 0, -1, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782269
    {'cdim': 5, 'counter': 32, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.5n', 'multiplicity': 1, 'nt': [12, 219], 'qdim': 5, 'qvalues': [5, 5, -5, -5, -1, 3, 1, 1, -3, 1, 3, -1, -3, -1, -1, 1, 5, 5, 5, 5, -1, 2, -1, 2, 2, -1, 2, -1, 2, -1, 1, -1, -1, 1, -1, -1, 1, 1, 0, 5, -5, -5, -1, 3, 3, -1, 1, -1, 3, -1, 0, -1, 3, -1, 0, 1, -3, 1, 1, -1, 1, -3, 3, -2, 1, -1, -2, 2, 1, 1, -1, 2, 0, 1, -1, 0, 1, -1, -2, -2, 1, -1, -1, 0, 1, 0, 0, 1, -1, 0, -1, 0, 0, 1, -1, 0, 1, 0, 0, 0, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782270
    {'cdim': 5, 'counter': 33, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.5o', 'multiplicity': 1, 'nt': [12, 219], 'qdim': 5, 'qvalues': [5, 5, -5, -5, 1, -3, 1, -1, 3, -1, -3, 1, 3, -1, -1, 1, 5, 5, 5, 5, -1, 2, -1, 2, 2, -1, 2, -1, 2, -1, -1, -1, 1, -1, 1, -1, 1, 1, 0, 5, -5, -5, 1, -3, -3, 1, 1, 1, -3, 1, 0, 1, -3, 1, 0, -1, 3, 1, -1, 1, 1, 3, -3, -2, 1, -1, -2, 2, 1, 1, 1, 2, 0, 1, -1, 0, 1, 1, -2, -2, 1, -1, -1, 0, -1, 0, 0, -1, 1, 0, 1, 0, 0, -1, 1, 0, -1, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782271
    {'cdim': 5, 'counter': 34, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.5p', 'multiplicity': 1, 'nt': [12, 219], 'qdim': 5, 'qvalues': [5, 5, -5, -5, 3, -1, 1, -3, 1, -3, -1, 3, 1, -1, -1, 1, 5, 5, 5, 5, 2, -1, 2, -1, -1, 2, -1, 2, -1, 2, 1, -1, -1, 1, -1, -1, 1, 1, 0, 5, -5, -5, 3, -1, -1, 3, 1, 3, -1, 0, -1, 3, -1, 0, -1, -3, 1, 1, -3, 3, 1, 1, -1, 1, -2, 2, 1, -1, -2, 1, 0, -1, -1, -2, 2, -1, -2, 0, 1, 1, 1, -1, -1, 1, 0, 1, -1, 0, 0, -1, 0, -1, 1, 0, 0, 1, 0, 0, 0, 0, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782272
    {'cdim': 6, 'counter': 35, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.6a', 'multiplicity': 1, 'nt': [9, 18], 'qdim': 6, 'qvalues': [6, 0, 0, 2, 6, 6, 6, 2, 2, 0, 0, 0, 0, 0, 2, 0, -3, 0, 0, 0, 6, 6, -3, -3, 0, 0, 0, 0, 0, 0, 6, 6, 2, 0, 0, 0, 0, 2, 6, 0, 0, -1, -3, -3, 0, 0, -3, 0, 0, 6, 6, 0, 0, -3, -3, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 2, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 2, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, -3, 0, 0, 0, 0, -1, 0], 'schur_index': 1}
  • id: 16782273
    {'cdim': 6, 'counter': 36, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.6b', 'multiplicity': 1, 'nt': [18, 51], 'qdim': 6, 'qvalues': [6, 0, 0, -2, 6, 6, 6, -2, -2, 0, 0, 0, 0, 0, -2, 0, -3, 0, 0, 0, 6, 6, -3, -3, 0, 0, 0, 0, 0, 0, 6, 6, -2, 0, 0, 0, 0, -2, 6, 0, 0, 1, -3, -3, 0, 0, -3, 0, 0, 6, 6, 0, 0, -3, -3, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, -2, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, -2, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, -3, 0, 0, 0, 0, 1, 0], 'schur_index': 1}
  • id: 16782274
    {'cdim': 6, 'counter': 37, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.6c', 'multiplicity': 1, 'nt': [18, 94], 'qdim': 6, 'qvalues': [6, 0, 0, -2, -6, -6, 6, 2, 2, 0, 0, 0, 0, 0, -2, 0, -3, 0, 0, 0, 6, 6, -3, -3, 0, 0, 0, 0, 0, 0, -6, 6, 2, 0, 0, 0, 0, -2, 6, 0, 0, 1, 3, 3, 0, 0, -3, 0, 0, -6, -6, 0, 0, 3, 3, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -2, 0, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, -3, 0, 0, 0, 0, 1, 0], 'schur_index': 1}
  • id: 16782275
    {'cdim': 6, 'counter': 38, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.6d', 'multiplicity': 1, 'nt': [18, 94], 'qdim': 6, 'qvalues': [6, 0, 0, 2, -6, -6, 6, -2, -2, 0, 0, 0, 0, 0, 2, 0, -3, 0, 0, 0, 6, 6, -3, -3, 0, 0, 0, 0, 0, 0, -6, 6, -2, 0, 0, 0, 0, 2, 6, 0, 0, -1, 3, 3, 0, 0, -3, 0, 0, -6, -6, 0, 0, 3, 3, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, -2, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, -3, 0, 0, 0, 0, -1, 0], 'schur_index': 1}
  • id: 16782276
    {'cdim': 9, 'counter': 39, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.9a', 'multiplicity': 1, 'nt': [10, 32], 'qdim': 9, 'qvalues': [9, 9, 9, 9, 3, 3, 1, 3, 3, 3, 3, 3, 3, 1, 1, 1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, -1, -1, 1, 1, 1, -1, 9, 9, 9, 3, 3, 3, 3, 1, 3, 3, 0, 0, 3, 3, 0, 0, 3, 3, 1, 3, 3, 1, 3, 3, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 16782278
    {'cdim': 9, 'counter': 40, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.9b', 'multiplicity': 1, 'nt': [20, 145], 'qdim': 9, 'qvalues': [9, 9, 9, 9, -3, -3, 1, -3, -3, -3, -3, -3, -3, 1, 1, 1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, -1, 9, 9, 9, -3, -3, -3, -3, 1, -3, -3, 0, 0, -3, -3, 0, 0, -3, -3, 1, -3, -3, 1, -3, -3, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 16782279
    {'cdim': 9, 'counter': 41, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.9c', 'multiplicity': 1, 'nt': [20, 199], 'qdim': 9, 'qvalues': [9, -9, -9, 9, -3, -3, 1, -3, -3, 3, 3, 3, 3, -1, 1, -1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, -1, -1, -1, -1, 1, -1, -9, -9, 9, -3, -3, -3, -3, 1, -3, -3, 0, 0, -3, -3, 0, 0, 3, 3, 1, -3, 3, 1, -3, 3, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 16782280
    {'cdim': 9, 'counter': 42, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.9d', 'multiplicity': 1, 'nt': [20, 199], 'qdim': 9, 'qvalues': [9, -9, -9, 9, 3, 3, 1, 3, 3, -3, -3, -3, -3, -1, 1, -1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, 1, -1, -1, 1, -1, -9, -9, 9, 3, 3, 3, 3, 1, 3, 3, 0, 0, 3, 3, 0, 0, -3, -3, 1, 3, -3, 1, 3, -3, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 16782281
    {'cdim': 9, 'counter': 43, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.9e', 'multiplicity': 1, 'nt': [20, 199], 'qdim': 9, 'qvalues': [9, -9, 9, -9, -3, -3, 1, 3, 3, -3, 3, 3, -3, 1, -1, -1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, 1, -1, 1, -1, -1, -9, 9, -9, -3, -3, -3, -3, 1, -3, -3, 0, 0, -3, -3, 0, 0, -3, -3, 1, 3, 3, 1, 3, 3, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 16782282
    {'cdim': 9, 'counter': 44, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.9f', 'multiplicity': 1, 'nt': [20, 199], 'qdim': 9, 'qvalues': [9, -9, 9, -9, 3, 3, 1, -3, -3, 3, -3, -3, 3, 1, -1, -1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 1, -1, -1, 1, -1, -1, -9, 9, -9, 3, 3, 3, 3, 1, 3, 3, 0, 0, 3, 3, 0, 0, 3, 3, 1, -3, -3, 1, -3, -3, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 16782283
    {'cdim': 9, 'counter': 45, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.9g', 'multiplicity': 1, 'nt': [20, 199], 'qdim': 9, 'qvalues': [9, 9, -9, -9, -3, -3, 1, 3, 3, 3, -3, -3, 3, -1, -1, 1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, 1, -1, 1, -1, -1, -1, 9, -9, -9, -3, -3, -3, -3, 1, -3, -3, 0, 0, -3, -3, 0, 0, 3, 3, 1, 3, -3, 1, 3, -3, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 16782284
    {'cdim': 9, 'counter': 46, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.9h', 'multiplicity': 1, 'nt': [20, 199], 'qdim': 9, 'qvalues': [9, 9, -9, -9, 3, 3, 1, -3, -3, -3, 3, 3, -3, -1, -1, 1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, -1, 1, 1, -1, -1, -1, 9, -9, -9, 3, 3, 3, 3, 1, 3, 3, 0, 0, 3, 3, 0, 0, -3, -3, 1, -3, 3, 1, -3, 3, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 16782285
    {'cdim': 10, 'counter': 47, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.10a', 'multiplicity': 1, 'nt': [18, 452], 'qdim': 10, 'qvalues': [10, 0, 10, 0, -2, 6, 2, 0, 0, -2, 0, 0, 6, 2, 0, 0, 10, 10, -5, -5, -2, 4, -2, 4, -2, 1, 4, -2, -2, 1, 2, -2, 0, 0, 2, 0, -2, 0, 0, 0, -5, 0, -2, 6, -3, 1, 2, -2, 6, -2, 0, 1, -3, -2, 0, 1, -3, -1, 0, 0, 2, 0, 0, 4, -2, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 1, -2, 0, -2, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, 1, -1, 1, -1, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782286
    {'cdim': 10, 'counter': 48, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.10b', 'multiplicity': 1, 'nt': [18, 452], 'qdim': 10, 'qvalues': [10, 0, 10, 0, 6, -2, 2, 0, 0, 6, 0, 0, -2, 2, 0, 0, 10, 10, -5, -5, 4, -2, 4, -2, 1, -2, -2, 4, 1, -2, 2, -2, 0, 0, 2, 0, -2, 0, 0, 0, -5, 0, 6, -2, 1, -3, 2, 6, -2, 0, -2, -3, 1, 0, -2, -3, 1, -1, 0, 0, 2, 0, 0, -2, 4, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 1, -2, 0, 0, 1, 0, -1, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, -2, -2, 2, 1, -1, 1, -1, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782287
    {'cdim': 10, 'counter': 49, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.10c', 'multiplicity': 1, 'nt': [18, 452], 'qdim': 10, 'qvalues': [10, 10, 0, 0, -2, 6, 2, 0, 0, 0, 6, -2, 0, 0, 0, 2, 10, -5, 10, -5, -2, 4, -2, 4, 4, -2, -2, 1, -2, 1, 2, -2, 0, 2, 0, -2, 0, 0, 0, -5, 0, 0, -2, 6, 6, -2, 2, 1, -3, -2, 0, 1, -3, -2, 0, 0, 0, 2, 0, 1, -1, 0, -3, 0, 0, -2, 0, 4, 0, -1, -2, -2, 0, 0, 1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, -2, 1, -1, -2, 2, 1, -1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782289
    {'cdim': 10, 'counter': 50, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.10d', 'multiplicity': 1, 'nt': [18, 452], 'qdim': 10, 'qvalues': [10, 10, 0, 0, 6, -2, 2, 0, 0, 0, -2, 6, 0, 0, 0, 2, 10, -5, 10, -5, 4, -2, 4, -2, -2, 4, 1, -2, 1, -2, 2, -2, 0, 2, 0, -2, 0, 0, 0, -5, 0, 0, 6, -2, -2, 6, 2, -3, 1, 0, -2, -3, 1, 0, -2, 0, 0, 2, 0, -3, -1, 0, 1, 0, 0, 4, 0, -2, 0, -1, 0, 1, 1, 0, -2, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 1, -1, -2, 2, 1, -1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782290
    {'cdim': 10, 'counter': 51, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.10e', 'multiplicity': 1, 'nt': [30, 164], 'qdim': 10, 'qvalues': [10, 10, 10, 10, -2, 2, -2, -2, 2, -2, 2, -2, 2, -2, -2, -2, 10, 10, 10, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 10, 10, -2, 2, 2, -2, -2, -2, 2, 1, -1, -2, 2, 1, -1, -2, 2, -2, -2, -2, -2, 2, 2, 1, 1, 1, 1, 1, 1, -2, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -2, -2, -2, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782291
    {'cdim': 10, 'counter': 52, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.10f', 'multiplicity': 1, 'nt': [30, 164], 'qdim': 10, 'qvalues': [10, 10, 10, 10, 2, -2, -2, 2, -2, 2, -2, 2, -2, -2, -2, -2, 10, 10, 10, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 10, 10, 2, -2, -2, 2, -2, 2, -2, -1, 1, 2, -2, -1, 1, 2, -2, -2, 2, 2, -2, -2, -2, 1, 1, 1, 1, 1, 1, -2, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -2, -2, -2, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782292
    {'cdim': 10, 'counter': 53, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.10g', 'multiplicity': 1, 'nt': [30, 261], 'qdim': 10, 'qvalues': [10, -10, -10, 10, -2, 2, -2, -2, 2, 2, -2, 2, -2, 2, -2, 2, 10, 10, 10, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, -10, 10, -2, 2, 2, -2, -2, -2, 2, 1, -1, -2, 2, 1, -1, 2, -2, -2, -2, 2, -2, 2, -2, -1, -1, -1, 1, -1, 1, -2, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 2, 2, -2, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782293
    {'cdim': 10, 'counter': 54, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.10h', 'multiplicity': 1, 'nt': [30, 261], 'qdim': 10, 'qvalues': [10, -10, -10, 10, 2, -2, -2, 2, -2, -2, 2, -2, 2, 2, -2, 2, 10, 10, 10, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, -10, 10, 2, -2, -2, 2, -2, 2, -2, -1, 1, 2, -2, -1, 1, -2, 2, -2, 2, -2, -2, -2, 2, -1, -1, -1, 1, -1, 1, -2, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 2, 2, -2, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782294
    {'cdim': 10, 'counter': 55, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.10i', 'multiplicity': 1, 'nt': [30, 261], 'qdim': 10, 'qvalues': [10, -10, 10, -10, -2, 2, -2, 2, -2, -2, -2, 2, 2, -2, 2, 2, 10, 10, 10, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 10, -10, -2, 2, 2, -2, -2, -2, 2, 1, -1, -2, 2, 1, -1, -2, 2, -2, 2, 2, -2, -2, -2, 1, 1, -1, -1, -1, -1, -2, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 2, -2, 2, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782295
    {'cdim': 10, 'counter': 56, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.10j', 'multiplicity': 1, 'nt': [30, 261], 'qdim': 10, 'qvalues': [10, -10, 10, -10, 2, -2, -2, -2, 2, 2, 2, -2, -2, -2, 2, 2, 10, 10, 10, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 10, -10, 2, -2, -2, 2, -2, 2, -2, -1, 1, 2, -2, -1, 1, 2, -2, -2, -2, -2, -2, 2, 2, 1, 1, -1, -1, -1, -1, -2, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 2, -2, 2, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782296
    {'cdim': 10, 'counter': 57, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.10k', 'multiplicity': 1, 'nt': [30, 261], 'qdim': 10, 'qvalues': [10, 10, -10, -10, -2, 2, -2, 2, -2, 2, 2, -2, -2, 2, 2, -2, 10, 10, 10, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, -10, -10, -2, 2, 2, -2, -2, -2, 2, 1, -1, -2, 2, 1, -1, 2, -2, -2, 2, -2, -2, -2, 2, -1, -1, 1, -1, 1, -1, -2, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, -2, 2, 2, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782297
    {'cdim': 10, 'counter': 58, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.10l', 'multiplicity': 1, 'nt': [30, 261], 'qdim': 10, 'qvalues': [10, 10, -10, -10, 2, -2, -2, -2, 2, -2, -2, 2, 2, 2, 2, -2, 10, 10, 10, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, -10, -10, 2, -2, -2, 2, -2, 2, -2, -1, 1, 2, -2, -1, 1, -2, 2, -2, -2, 2, -2, 2, -2, -1, -1, 1, -1, 1, -1, -2, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -2, 2, 2, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782298
    {'cdim': 10, 'counter': 59, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.10m', 'multiplicity': 1, 'nt': [36, 4986], 'qdim': 10, 'qvalues': [10, 0, 10, 0, -6, 2, 2, 0, 0, -6, 0, 0, 2, 2, 0, 0, 10, 10, -5, -5, 4, -2, 4, -2, 1, -2, -2, 4, 1, -2, -2, -2, 0, 0, -2, 0, -2, 0, 0, 0, -5, 0, -6, 2, -1, 3, 2, -6, 2, 0, 2, 3, -1, 0, 2, 3, -1, -1, 0, 0, 2, 0, 0, -2, 4, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, -1, -2, 0, 0, 1, 0, -1, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, -2, -2, -2, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782300
    {'cdim': 10, 'counter': 60, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.10n', 'multiplicity': 1, 'nt': [36, 4986], 'qdim': 10, 'qvalues': [10, 0, 10, 0, 2, -6, 2, 0, 0, 2, 0, 0, -6, 2, 0, 0, 10, 10, -5, -5, -2, 4, -2, 4, -2, 1, 4, -2, -2, 1, -2, -2, 0, 0, -2, 0, -2, 0, 0, 0, -5, 0, 2, -6, 3, -1, 2, 2, -6, 2, 0, -1, 3, 2, 0, -1, 3, -1, 0, 0, 2, 0, 0, 4, -2, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 1, 2, 0, -2, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782301
    {'cdim': 10, 'counter': 61, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.10o', 'multiplicity': 1, 'nt': [36, 4986], 'qdim': 10, 'qvalues': [10, 10, 0, 0, -6, 2, 2, 0, 0, 0, 2, -6, 0, 0, 0, 2, 10, -5, 10, -5, 4, -2, 4, -2, -2, 4, 1, -2, 1, -2, -2, -2, 0, -2, 0, -2, 0, 0, 0, -5, 0, 0, -6, 2, 2, -6, 2, 3, -1, 0, 2, 3, -1, 0, 2, 0, 0, 2, 0, 3, -1, 0, -1, 0, 0, 4, 0, -2, 0, -1, 0, 1, -1, 0, -2, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 1, -2, -2, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782302
    {'cdim': 10, 'counter': 62, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.10p', 'multiplicity': 1, 'nt': [36, 4986], 'qdim': 10, 'qvalues': [10, 10, 0, 0, 2, -6, 2, 0, 0, 0, -6, 2, 0, 0, 0, 2, 10, -5, 10, -5, -2, 4, -2, 4, 4, -2, -2, 1, -2, 1, -2, -2, 0, -2, 0, -2, 0, 0, 0, -5, 0, 0, 2, -6, -6, 2, 2, -1, 3, 2, 0, -1, 3, 2, 0, 0, 0, 2, 0, -1, -1, 0, 3, 0, 0, -2, 0, 4, 0, -1, 2, -2, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, -2, 1, 1, -2, -2, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782303
    {'cdim': 10, 'counter': 63, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.10q', 'multiplicity': 1, 'nt': [36, 7407], 'qdim': 10, 'qvalues': [10, -10, 0, 0, -6, 2, 2, 0, 0, 0, -2, 6, 0, 0, 0, -2, 10, -5, 10, -5, 4, -2, 4, -2, -2, 4, 1, -2, 1, -2, -2, -2, 0, 2, 0, 2, 0, 0, 0, 5, 0, 0, -6, 2, 2, -6, 2, 3, -1, 0, 2, 3, -1, 0, 2, 0, 0, 2, 0, -3, -1, 0, 1, 0, 0, -4, 0, 2, 0, -1, 0, -1, -1, 0, 2, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 1, -2, -2, 1, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782304
    {'cdim': 10, 'counter': 64, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.10r', 'multiplicity': 1, 'nt': [36, 7407], 'qdim': 10, 'qvalues': [10, -10, 0, 0, -2, 6, 2, 0, 0, 0, -6, 2, 0, 0, 0, -2, 10, -5, 10, -5, -2, 4, -2, 4, 4, -2, -2, 1, -2, 1, 2, -2, 0, -2, 0, 2, 0, 0, 0, 5, 0, 0, -2, 6, 6, -2, 2, 1, -3, -2, 0, 1, -3, -2, 0, 0, 0, 2, 0, -1, -1, 0, 3, 0, 0, 2, 0, -4, 0, -1, -2, 2, 0, 0, -1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, -2, 1, -1, -2, 2, 1, -1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782305
    {'cdim': 10, 'counter': 65, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.10s', 'multiplicity': 1, 'nt': [36, 7407], 'qdim': 10, 'qvalues': [10, -10, 0, 0, 2, -6, 2, 0, 0, 0, 6, -2, 0, 0, 0, -2, 10, -5, 10, -5, -2, 4, -2, 4, 4, -2, -2, 1, -2, 1, -2, -2, 0, 2, 0, 2, 0, 0, 0, 5, 0, 0, 2, -6, -6, 2, 2, -1, 3, 2, 0, -1, 3, 2, 0, 0, 0, 2, 0, 1, -1, 0, -3, 0, 0, 2, 0, -4, 0, -1, 2, 2, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, -2, 1, 1, -2, -2, 1, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782306
    {'cdim': 10, 'counter': 66, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.10t', 'multiplicity': 1, 'nt': [36, 7407], 'qdim': 10, 'qvalues': [10, -10, 0, 0, 6, -2, 2, 0, 0, 0, 2, -6, 0, 0, 0, -2, 10, -5, 10, -5, 4, -2, 4, -2, -2, 4, 1, -2, 1, -2, 2, -2, 0, -2, 0, 2, 0, 0, 0, 5, 0, 0, 6, -2, -2, 6, 2, -3, 1, 0, -2, -3, 1, 0, -2, 0, 0, 2, 0, 3, -1, 0, -1, 0, 0, -4, 0, 2, 0, -1, 0, -1, 1, 0, 2, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 1, -1, -2, 2, 1, -1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782307
    {'cdim': 10, 'counter': 67, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.10u', 'multiplicity': 1, 'nt': [36, 7407], 'qdim': 10, 'qvalues': [10, 0, -10, 0, -6, 2, 2, 0, 0, 6, 0, 0, -2, -2, 0, 0, 10, 10, -5, -5, 4, -2, 4, -2, 1, -2, -2, 4, 1, -2, -2, -2, 0, 0, 2, 0, 2, 0, 0, 0, 5, 0, -6, 2, -1, 3, 2, -6, 2, 0, 2, 3, -1, 0, 2, -3, 1, -1, 0, 0, 2, 0, 0, 2, -4, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, -1, 2, 0, 0, -1, 0, 1, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, -2, -2, -2, 1, 1, 1, 1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782308
    {'cdim': 10, 'counter': 68, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.10v', 'multiplicity': 1, 'nt': [36, 7407], 'qdim': 10, 'qvalues': [10, 0, -10, 0, -2, 6, 2, 0, 0, 2, 0, 0, -6, -2, 0, 0, 10, 10, -5, -5, -2, 4, -2, 4, -2, 1, 4, -2, -2, 1, 2, -2, 0, 0, -2, 0, 2, 0, 0, 0, 5, 0, -2, 6, -3, 1, 2, -2, 6, -2, 0, 1, -3, -2, 0, -1, 3, -1, 0, 0, 2, 0, 0, -4, 2, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, -2, 0, 2, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, 1, -1, 1, -1, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782309
    {'cdim': 10, 'counter': 69, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.10w', 'multiplicity': 1, 'nt': [36, 7407], 'qdim': 10, 'qvalues': [10, 0, -10, 0, 2, -6, 2, 0, 0, -2, 0, 0, 6, -2, 0, 0, 10, 10, -5, -5, -2, 4, -2, 4, -2, 1, 4, -2, -2, 1, -2, -2, 0, 0, 2, 0, 2, 0, 0, 0, 5, 0, 2, -6, 3, -1, 2, 2, -6, 2, 0, -1, 3, 2, 0, 1, -3, -1, 0, 0, 2, 0, 0, -4, 2, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, -1, 2, 0, 2, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 1, 1, 1, 1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782311
    {'cdim': 10, 'counter': 70, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.10x', 'multiplicity': 1, 'nt': [36, 7407], 'qdim': 10, 'qvalues': [10, 0, -10, 0, 6, -2, 2, 0, 0, -6, 0, 0, 2, -2, 0, 0, 10, 10, -5, -5, 4, -2, 4, -2, 1, -2, -2, 4, 1, -2, 2, -2, 0, 0, -2, 0, 2, 0, 0, 0, 5, 0, 6, -2, 1, -3, 2, 6, -2, 0, -2, -3, 1, 0, -2, 3, -1, -1, 0, 0, 2, 0, 0, 2, -4, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 1, 2, 0, 0, -1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, -2, -2, 2, 1, -1, 1, -1, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782312
    {'cdim': 16, 'counter': 71, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.16a', 'multiplicity': 1, 'nt': [36, 1252], 'qdim': 16, 'qvalues': [16, 16, 16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 16, 16, 16, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 16, 16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 0, 0, -2, 0, -2, -2, 0, -2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 16782313
    {'cdim': 16, 'counter': 72, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.16b', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 16, 'qvalues': [16, -16, -16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 16, 16, 16, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, -16, -16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, 2, -2, 0, 0, 2, 0, -2, 2, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 16782314
    {'cdim': 16, 'counter': 73, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.16c', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 16, 'qvalues': [16, -16, 16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 16, 16, 16, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, -16, 16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, -2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 16782315
    {'cdim': 16, 'counter': 74, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.16d', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 16, 'qvalues': [16, 16, -16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 16, 16, 16, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 16, -16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 2, -2, 2, 0, 0, -2, 0, 2, -2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 16782316
    {'cdim': 18, 'counter': 75, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.18a', 'multiplicity': 1, 'nt': [30, 535], 'qdim': 18, 'qvalues': [18, 0, 18, 0, 6, 6, 2, 0, 0, 6, 0, 0, 6, 2, 0, 0, 18, 18, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, -2, 0, 2, 0, -2, 0, -9, 0, 6, 6, -3, -3, 2, 6, 6, 0, 0, -3, -3, 0, 0, -3, -3, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 2, 2, -2, -1, 1, -1, 1, 1, 0, 0, 0, -1, 0, -2, 1, -2, 1, 1, 0, 0], 'schur_index': 1}
  • id: 16782317
    {'cdim': 18, 'counter': 76, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.18b', 'multiplicity': 1, 'nt': [30, 535], 'qdim': 18, 'qvalues': [18, 18, 0, 0, 6, 6, 2, 0, 0, 0, 6, 6, 0, 0, 0, 2, 18, -9, 18, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, -2, 0, 2, 0, 0, -2, -9, 0, 0, 6, 6, 6, 6, 2, -3, -3, 0, 0, -3, -3, 0, 0, 0, 0, 2, 0, -3, -1, 0, -3, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, -1, 1, 2, -2, -1, 1, 0, 1, -1, 0, 0, 0, -2, -2, 1, 1, 0, 0, 1], 'schur_index': 1}
  • id: 16782318
    {'cdim': 18, 'counter': 77, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.18c', 'multiplicity': 1, 'nt': [60, 0], 'qdim': 18, 'qvalues': [18, -18, 0, 0, -6, -6, 2, 0, 0, 0, 6, 6, 0, 0, 0, -2, 18, -9, 18, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, -2, 0, -2, 0, 0, -2, 9, 0, 0, -6, -6, -6, -6, 2, 3, 3, 0, 0, 3, 3, 0, 0, 0, 0, 2, 0, -3, -1, 0, -3, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -1, -1, 2, 2, -1, -1, 0, 1, 1, 0, 0, 0, -2, -2, 1, 1, 0, 0, -1], 'schur_index': 1}
  • id: 16782319
    {'cdim': 18, 'counter': 78, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.18d', 'multiplicity': 1, 'nt': [60, 0], 'qdim': 18, 'qvalues': [18, -18, 0, 0, 6, 6, 2, 0, 0, 0, -6, -6, 0, 0, 0, -2, 18, -9, 18, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 2, 0, -2, 0, 0, -2, 9, 0, 0, 6, 6, 6, 6, 2, -3, -3, 0, 0, -3, -3, 0, 0, 0, 0, 2, 0, 3, -1, 0, 3, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, -1, 1, 2, -2, -1, 1, 0, -1, 1, 0, 0, 0, -2, -2, 1, 1, 0, 0, -1], 'schur_index': 1}
  • id: 16782320
    {'cdim': 18, 'counter': 79, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.18e', 'multiplicity': 1, 'nt': [60, 0], 'qdim': 18, 'qvalues': [18, 0, -18, 0, -6, -6, 2, 0, 0, 6, 0, 0, 6, -2, 0, 0, 18, 18, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, 0, -2, 0, -2, 0, 9, 0, -6, -6, 3, 3, 2, -6, -6, 0, 0, 3, 3, 0, 0, -3, -3, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, 1, 0, 0, 0, 1, 0, -2, 1, -2, 1, -1, 0, 0], 'schur_index': 1}
  • id: 16782322
    {'cdim': 18, 'counter': 80, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.18f', 'multiplicity': 1, 'nt': [60, 0], 'qdim': 18, 'qvalues': [18, 0, -18, 0, 6, 6, 2, 0, 0, -6, 0, 0, -6, -2, 0, 0, 18, 18, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 2, 0, -2, 0, -2, 0, 9, 0, 6, 6, -3, -3, 2, 6, 6, 0, 0, -3, -3, 0, 0, 3, 3, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 2, 2, -2, -1, 1, -1, 1, -1, 0, 0, 0, 1, 0, -2, 1, -2, 1, -1, 0, 0], 'schur_index': 1}
  • id: 16782323
    {'cdim': 18, 'counter': 81, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.18g', 'multiplicity': 1, 'nt': [60, 0], 'qdim': 18, 'qvalues': [18, 0, 18, 0, -6, -6, 2, 0, 0, -6, 0, 0, -6, 2, 0, 0, 18, 18, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, -2, 0, -9, 0, -6, -6, 3, 3, 2, -6, -6, 0, 0, 3, 3, 0, 0, 3, 3, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, -1, 0, 0, 0, -1, 0, -2, 1, -2, 1, 1, 0, 0], 'schur_index': 1}
  • id: 16782324
    {'cdim': 18, 'counter': 82, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.18h', 'multiplicity': 1, 'nt': [60, 0], 'qdim': 18, 'qvalues': [18, 18, 0, 0, -6, -6, 2, 0, 0, 0, -6, -6, 0, 0, 0, 2, 18, -9, 18, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, -2, -9, 0, 0, -6, -6, -6, -6, 2, 3, 3, 0, 0, 3, 3, 0, 0, 0, 0, 2, 0, 3, -1, 0, 3, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, -1, -1, 2, 2, -1, -1, 0, -1, -1, 0, 0, 0, -2, -2, 1, 1, 0, 0, 1], 'schur_index': 1}
  • id: 16782325
    {'cdim': 20, 'counter': 83, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.20a', 'multiplicity': 1, 'nt': [36, 12773], 'qdim': 20, 'qvalues': [20, 0, 0, 0, -4, 12, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, -10, -10, 5, -4, 8, -4, 8, -4, 2, -4, 2, 2, -1, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 12, -6, 2, 4, 2, -6, -4, 0, -1, 3, -4, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 2, -2, 2, -2, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782326
    {'cdim': 20, 'counter': 84, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.20b', 'multiplicity': 1, 'nt': [36, 12773], 'qdim': 20, 'qvalues': [20, 0, 0, 0, 12, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, -10, -10, 5, 8, -4, 8, -4, 2, -4, 2, -4, -1, 2, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, -4, 2, -6, 4, -6, 2, 0, -4, 3, -1, 0, -4, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 2, -2, 2, -2, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782327
    {'cdim': 20, 'counter': 85, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.20c', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 20, 'qvalues': [20, 0, 0, 0, -12, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, -10, -10, 5, 8, -4, 8, -4, 2, -4, 2, -4, -1, 2, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 4, -2, 6, 4, 6, -2, 0, 4, -3, 1, 0, 4, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782328
    {'cdim': 20, 'counter': 86, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.20d', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 20, 'qvalues': [20, 0, 0, 0, 4, -12, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, -10, -10, 5, -4, 8, -4, 8, -4, 2, -4, 2, 2, -1, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -12, 6, -2, 4, -2, 6, 4, 0, 1, -3, 4, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782329
    {'cdim': 20, 'counter': 87, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.20e', 'multiplicity': 1, 'nt': [90, 0], 'qdim': 20, 'qvalues': [20, -20, 0, 0, -4, 4, -4, 0, 0, 0, -4, 4, 0, 0, 0, 4, 20, -10, 20, -10, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, -4, 4, 4, -4, -4, 2, -2, 2, -2, 2, -2, 2, -2, 0, 0, -4, 0, -2, 2, 0, 2, 0, 0, -2, 0, -2, 0, 2, 2, 1, 1, 0, 1, -2, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, -2, 1, -1, -1, 0, 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], 'schur_index': 1}
  • id: 16782330
    {'cdim': 20, 'counter': 88, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.20f', 'multiplicity': 1, 'nt': [90, 0], 'qdim': 20, 'qvalues': [20, -20, 0, 0, 4, -4, -4, 0, 0, 0, 4, -4, 0, 0, 0, 4, 20, -10, 20, -10, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 4, -4, -4, 4, -4, -2, 2, -2, 2, -2, 2, -2, 2, 0, 0, -4, 0, 2, 2, 0, -2, 0, 0, -2, 0, -2, 0, 2, -2, 1, -1, 0, 1, 2, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 2, -1, 1, 1, 0, 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], 'schur_index': 1}
  • id: 16782331
    {'cdim': 20, 'counter': 89, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.20g', 'multiplicity': 1, 'nt': [90, 0], 'qdim': 20, 'qvalues': [20, 0, -20, 0, -4, 4, -4, 0, 0, 4, 0, 0, -4, 4, 0, 0, 20, 20, -10, -10, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, -4, 4, -2, 2, -4, -4, 4, 2, -2, 2, -2, 2, -2, -2, 2, 2, 0, 0, -4, 0, 0, -2, -2, 0, 0, 0, 0, 2, -1, 0, -2, 0, 0, 1, 1, 2, 0, 1, 0, -2, 0, 2, -2, 0, 0, 0, 0, 1, -1, 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], 'schur_index': 1}
  • id: 16782333
    {'cdim': 20, 'counter': 90, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.20h', 'multiplicity': 1, 'nt': [90, 0], 'qdim': 20, 'qvalues': [20, 0, -20, 0, 4, -4, -4, 0, 0, -4, 0, 0, 4, 4, 0, 0, 20, 20, -10, -10, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 4, -4, 2, -2, -4, 4, -4, -2, 2, -2, 2, -2, 2, 2, -2, 2, 0, 0, -4, 0, 0, -2, -2, 0, 0, 0, 0, 2, 1, 0, 2, 0, 0, -1, 1, -2, 0, 1, 0, -2, 0, -2, 2, 0, 0, 0, 0, -1, 1, 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], 'schur_index': 1}
  • id: 16782334
    {'cdim': 20, 'counter': 91, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.20i', 'multiplicity': 1, 'nt': [90, 0], 'qdim': 20, 'qvalues': [20, 0, 20, 0, -4, 4, -4, 0, 0, -4, 0, 0, 4, -4, 0, 0, 20, 20, -10, -10, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, -4, 4, -2, 2, -4, -4, 4, 2, -2, 2, -2, 2, -2, 2, -2, 2, 0, 0, -4, 0, 0, 2, 2, 0, 0, 0, 0, 2, -1, 0, -2, 0, 0, 1, -1, 2, 0, -1, 0, 2, 0, -2, 2, 0, 0, 0, 0, 1, -1, 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], 'schur_index': 1}
  • id: 16782335
    {'cdim': 20, 'counter': 92, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.20j', 'multiplicity': 1, 'nt': [90, 0], 'qdim': 20, 'qvalues': [20, 0, 20, 0, 4, -4, -4, 0, 0, 4, 0, 0, -4, -4, 0, 0, 20, 20, -10, -10, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 4, -4, 2, -2, -4, 4, -4, -2, 2, -2, 2, -2, 2, -2, 2, 2, 0, 0, -4, 0, 0, 2, 2, 0, 0, 0, 0, 2, 1, 0, 2, 0, 0, -1, -1, -2, 0, -1, 0, 2, 0, 2, -2, 0, 0, 0, 0, -1, 1, 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], 'schur_index': 1}
  • id: 16782336
    {'cdim': 20, 'counter': 93, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.20k', 'multiplicity': 1, 'nt': [90, 0], 'qdim': 20, 'qvalues': [20, 20, 0, 0, -4, 4, -4, 0, 0, 0, 4, -4, 0, 0, 0, -4, 20, -10, 20, -10, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, -4, 4, 4, -4, -4, 2, -2, 2, -2, 2, -2, 2, -2, 0, 0, -4, 0, 2, 2, 0, -2, 0, 0, 2, 0, 2, 0, 2, 2, -1, 1, 0, -1, -2, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 2, 1, -1, 1, 0, 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], 'schur_index': 1}
  • id: 16782337
    {'cdim': 20, 'counter': 94, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.20l', 'multiplicity': 1, 'nt': [90, 0], 'qdim': 20, 'qvalues': [20, 20, 0, 0, 4, -4, -4, 0, 0, 0, -4, 4, 0, 0, 0, -4, 20, -10, 20, -10, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 4, -4, -4, 4, -4, -2, 2, -2, 2, -2, 2, -2, 2, 0, 0, -4, 0, -2, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, -2, -1, -1, 0, -1, 2, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, -2, -1, 1, -1, 0, 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], 'schur_index': 1}
  • id: 16782338
    {'cdim': 30, 'counter': 95, 'faithful': True, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.30a', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 30, 'qvalues': [30, 0, 0, 10, -6, 18, 6, -2, 6, 0, 0, 0, 0, 0, 2, 0, -15, 0, 0, 0, -6, 12, 3, -6, 0, 0, 0, 0, 0, 0, 6, -6, 2, 0, 0, 0, 0, -2, 0, 0, 0, -5, 3, -9, 0, 0, -3, 0, 0, -6, 0, 0, 0, 3, 0, 0, 0, 0, 1, 0, 0, -3, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782339
    {'cdim': 30, 'counter': 96, 'faithful': True, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.30b', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 30, 'qvalues': [30, 0, 0, 10, 18, -6, 6, 6, -2, 0, 0, 0, 0, 0, 2, 0, -15, 0, 0, 0, 12, -6, -6, 3, 0, 0, 0, 0, 0, 0, 6, -6, 2, 0, 0, 0, 0, -2, 0, 0, 0, -5, -9, 3, 0, 0, -3, 0, 0, 0, -6, 0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 1, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782340
    {'cdim': 30, 'counter': 97, 'faithful': True, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.30c', 'multiplicity': 1, 'nt': [108, 0], 'qdim': 30, 'qvalues': [30, 0, 0, -10, -18, 6, 6, 6, -2, 0, 0, 0, 0, 0, -2, 0, -15, 0, 0, 0, 12, -6, -6, 3, 0, 0, 0, 0, 0, 0, -6, -6, 2, 0, 0, 0, 0, 2, 0, 0, 0, 5, 9, -3, 0, 0, -3, 0, 0, 0, 6, 0, 0, 0, -3, 0, 0, 0, -3, 0, 0, 1, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782341
    {'cdim': 30, 'counter': 98, 'faithful': True, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.30d', 'multiplicity': 1, 'nt': [108, 0], 'qdim': 30, 'qvalues': [30, 0, 0, -10, -6, 18, 6, 2, -6, 0, 0, 0, 0, 0, -2, 0, -15, 0, 0, 0, -6, 12, 3, -6, 0, 0, 0, 0, 0, 0, 6, -6, -2, 0, 0, 0, 0, 2, 0, 0, 0, 5, 3, -9, 0, 0, -3, 0, 0, -6, 0, 0, 0, 3, 0, 0, 0, 0, -1, 0, 0, 3, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782342
    {'cdim': 30, 'counter': 99, 'faithful': True, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.30e', 'multiplicity': 1, 'nt': [108, 0], 'qdim': 30, 'qvalues': [30, 0, 0, -10, 6, -18, 6, -2, 6, 0, 0, 0, 0, 0, -2, 0, -15, 0, 0, 0, -6, 12, 3, -6, 0, 0, 0, 0, 0, 0, -6, -6, 2, 0, 0, 0, 0, 2, 0, 0, 0, 5, -3, 9, 0, 0, -3, 0, 0, 6, 0, 0, 0, -3, 0, 0, 0, 0, 1, 0, 0, -3, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782224
    {'cdim': 30, 'counter': 100, 'faithful': True, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.30f', 'multiplicity': 1, 'nt': [108, 0], 'qdim': 30, 'qvalues': [30, 0, 0, -10, 18, -6, 6, -6, 2, 0, 0, 0, 0, 0, -2, 0, -15, 0, 0, 0, 12, -6, -6, 3, 0, 0, 0, 0, 0, 0, 6, -6, -2, 0, 0, 0, 0, 2, 0, 0, 0, 5, -9, 3, 0, 0, -3, 0, 0, 0, -6, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, -1, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782225
    {'cdim': 30, 'counter': 101, 'faithful': True, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.30g', 'multiplicity': 1, 'nt': [108, 0], 'qdim': 30, 'qvalues': [30, 0, 0, 10, -18, 6, 6, -6, 2, 0, 0, 0, 0, 0, 2, 0, -15, 0, 0, 0, 12, -6, -6, 3, 0, 0, 0, 0, 0, 0, -6, -6, -2, 0, 0, 0, 0, -2, 0, 0, 0, -5, 9, -3, 0, 0, -3, 0, 0, 0, 6, 0, 0, 0, -3, 0, 0, 0, 3, 0, 0, -1, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782226
    {'cdim': 30, 'counter': 102, 'faithful': True, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.30h', 'multiplicity': 1, 'nt': [108, 0], 'qdim': 30, 'qvalues': [30, 0, 0, 10, 6, -18, 6, 2, -6, 0, 0, 0, 0, 0, 2, 0, -15, 0, 0, 0, -6, 12, 3, -6, 0, 0, 0, 0, 0, 0, -6, -6, -2, 0, 0, 0, 0, -2, 0, 0, 0, -5, -3, 9, 0, 0, -3, 0, 0, 6, 0, 0, 0, -3, 0, 0, 0, 0, -1, 0, 0, 3, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782227
    {'cdim': 32, 'counter': 103, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.32a', 'multiplicity': 1, 'nt': [90, 0], 'qdim': 32, 'qvalues': [32, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 32, -16, -16, -4, -4, -4, -4, 2, 2, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 2, -1, -1, 0, 0], 'schur_index': 1}
  • id: 16782228
    {'cdim': 32, 'counter': 104, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.32b', 'multiplicity': 1, 'nt': [90, 0], 'qdim': 32, 'qvalues': [32, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, -16, 32, -16, -4, -4, -4, -4, -4, -4, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -1, -1, 0, 0, -1], 'schur_index': 1}
  • id: 16782229
    {'cdim': 32, 'counter': 105, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.32c', 'multiplicity': 1, 'nt': [180, 0], 'qdim': 32, 'qvalues': [32, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, -16, 32, -16, -4, -4, -4, -4, -4, -4, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -1, -1, 0, 0, 1], 'schur_index': 1}
  • id: 16782230
    {'cdim': 32, 'counter': 106, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.32d', 'multiplicity': 1, 'nt': [180, 0], 'qdim': 32, 'qvalues': [32, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 32, -16, -16, -4, -4, -4, -4, 2, 2, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 2, -1, 1, 0, 0], 'schur_index': 1}
  • id: 16782231
    {'cdim': 36, 'counter': 107, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.36a', 'multiplicity': 1, 'nt': [60, 0], 'qdim': 36, 'qvalues': [36, 0, 0, 0, 12, 12, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, -18, -18, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 12, 12, -6, -6, 4, -6, -6, 0, 0, 3, 3, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -2, 2, -2, 2, 1, -1, 0, 0, 0, 0, 0, 0, -4, 2, 2, -1, 0, 0, 0], 'schur_index': 1}
  • id: 16782232
    {'cdim': 36, 'counter': 108, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.36b', 'multiplicity': 1, 'nt': [120, 0], 'qdim': 36, 'qvalues': [36, 0, 0, 0, -12, -12, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, -18, -18, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -12, -12, 6, 6, 4, 6, 6, 0, 0, -3, -3, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -2, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, -4, 2, 2, -1, 0, 0, 0], 'schur_index': 1}
  • id: 16782233
    {'cdim': 40, 'counter': 109, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.40a', 'multiplicity': 1, 'nt': [180, 0], 'qdim': 40, 'qvalues': [40, 0, 0, 0, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, -20, -20, 10, 4, 4, 4, 4, -2, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, -4, 4, -8, 4, -4, 4, -4, -2, 2, 4, -4, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 2, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782235
    {'cdim': 40, 'counter': 110, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.40b', 'multiplicity': 1, 'nt': [180, 0], 'qdim': 40, 'qvalues': [40, 0, 0, 0, 8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, -20, -20, 10, 4, 4, 4, 4, -2, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, 4, -4, -8, -4, 4, -4, 4, 2, -2, -4, 4, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, -2, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782236
    {'cdim': 54, 'counter': 111, 'faithful': True, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.54a', 'multiplicity': 1, 'nt': [90, 0], 'qdim': 54, 'qvalues': [54, 0, 0, 18, 18, 18, 6, 6, 6, 0, 0, 0, 0, 0, 2, 0, -27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 6, -2, 0, 0, 0, 0, 2, -6, 0, 0, -9, -9, -9, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 3, 0, 0, 0, 0, 1, 0], 'schur_index': 1}
  • id: 16782237
    {'cdim': 54, 'counter': 112, 'faithful': True, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.54b', 'multiplicity': 1, 'nt': [180, 0], 'qdim': 54, 'qvalues': [54, 0, 0, -18, -18, -18, 6, 6, 6, 0, 0, 0, 0, 0, -2, 0, -27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, -2, 0, 0, 0, 0, -2, -6, 0, 0, 9, 9, 9, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 3, 0, 0, 0, 0, -1, 0], 'schur_index': 1}
  • id: 16782238
    {'cdim': 54, 'counter': 113, 'faithful': True, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.54c', 'multiplicity': 1, 'nt': [180, 0], 'qdim': 54, 'qvalues': [54, 0, 0, -18, 18, 18, 6, -6, -6, 0, 0, 0, 0, 0, -2, 0, -27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 6, 2, 0, 0, 0, 0, -2, -6, 0, 0, 9, -9, -9, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 3, 0, 0, 0, 0, -1, 0], 'schur_index': 1}
  • id: 16782239
    {'cdim': 54, 'counter': 114, 'faithful': True, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.54d', 'multiplicity': 1, 'nt': [180, 0], 'qdim': 54, 'qvalues': [54, 0, 0, 18, -18, -18, 6, -6, -6, 0, 0, 0, 0, 0, 2, 0, -27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 2, 0, 0, 0, 0, 2, -6, 0, 0, -9, 9, 9, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 3, 0, 0, 0, 0, 1, 0], 'schur_index': 1}
  • id: 16782240
    {'cdim': 60, 'counter': 115, 'faithful': True, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.60a', 'multiplicity': 1, 'nt': [270, 0], 'qdim': 60, 'qvalues': [60, 0, 0, -20, -12, 12, -12, 4, -4, 0, 0, 0, 0, 0, 4, 0, -30, 0, 0, 0, 6, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 6, -6, 0, 0, 6, 0, 0, 6, -6, 0, 0, -3, 3, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 2, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782241
    {'cdim': 60, 'counter': 116, 'faithful': True, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.60b', 'multiplicity': 1, 'nt': [270, 0], 'qdim': 60, 'qvalues': [60, 0, 0, -20, 12, -12, -12, -4, 4, 0, 0, 0, 0, 0, 4, 0, -30, 0, 0, 0, 6, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, -6, 6, 0, 0, 6, 0, 0, -6, 6, 0, 0, 3, -3, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, -2, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782242
    {'cdim': 60, 'counter': 117, 'faithful': True, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.60c', 'multiplicity': 1, 'nt': [270, 0], 'qdim': 60, 'qvalues': [60, 0, 0, 20, -12, 12, -12, -4, 4, 0, 0, 0, 0, 0, -4, 0, -30, 0, 0, 0, 6, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 6, -6, 0, 0, 6, 0, 0, 6, -6, 0, 0, -3, 3, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782243
    {'cdim': 60, 'counter': 118, 'faithful': True, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.60d', 'multiplicity': 1, 'nt': [270, 0], 'qdim': 60, 'qvalues': [60, 0, 0, 20, 12, -12, -12, 4, -4, 0, 0, 0, 0, 0, -4, 0, -30, 0, 0, 0, 6, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, -6, 6, 0, 0, 6, 0, 0, -6, 6, 0, 0, 3, -3, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 2, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16782244
    {'cdim': 64, 'counter': 119, 'faithful': False, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.64a', 'multiplicity': 1, 'nt': [180, 0], 'qdim': 64, 'qvalues': [64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, -32, -32, 16, -8, -8, -8, -8, 4, 4, 4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, 1, 0, 0, 0], 'schur_index': 1}
  • id: 16782246
    {'cdim': 96, 'counter': 120, 'faithful': True, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.96a', 'multiplicity': 1, 'nt': [270, 0], 'qdim': 96, 'qvalues': [96, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, -12, -12, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, -1, 0], 'schur_index': 1}
  • id: 16782247
    {'cdim': 96, 'counter': 121, 'faithful': True, 'group': '77760.bo', 'group_order': 77760, 'image': None, 'label': '77760.bo.96b', 'multiplicity': 1, 'nt': [540, 0], 'qdim': 96, 'qvalues': [96, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, -12, -12, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 1, 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: 37056092
    {'center': '1.a1', 'center_index': 1, 'center_order': 77760, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 77760, 'label': '77760.bo.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 37056125
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  • id: 37056136
    {'center': '1.a1', 'center_index': 1, 'center_order': 77760, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 38880, 'label': '77760.bo.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-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: 37056147
    {'center': '1.a1', 'center_index': 1, 'center_order': 77760, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 38880, 'label': '77760.bo.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[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: 37056158
    {'center': '1.a1', 'center_index': 1, 'center_order': 77760, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 38880, 'label': '77760.bo.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-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: 37056169
    {'center': '1.a1', 'center_index': 1, 'center_order': 77760, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 38880, 'label': '77760.bo.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-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: 37056180
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  • id: 37056191
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  • id: 37056202
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  • id: 37056093
    {'center': '6.a1', 'center_index': 6, 'center_order': 12960, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 12960, 'label': '77760.bo.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 37056104
    {'center': '6.a1', 'center_index': 6, 'center_order': 12960, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1', 'kernel_order': 6480, 'label': '77760.bo.2c', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]]]}
  • id: 37056115
    {'center': '6.a1', 'center_index': 6, 'center_order': 12960, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1', 'kernel_order': 6480, 'label': '77760.bo.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]]]}
  • id: 37056118
    {'center': '6.a1', 'center_index': 6, 'center_order': 12960, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1', 'kernel_order': 6480, 'label': '77760.bo.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056119
    {'center': '6.a1', 'center_index': 6, 'center_order': 12960, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1', 'kernel_order': 6480, 'label': '77760.bo.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056120
    {'center': '6.a1', 'center_index': 6, 'center_order': 12960, 'counter': 15, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 6480, 'label': '77760.bo.2g', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056121
    {'center': '6.a1', 'center_index': 6, 'center_order': 12960, 'counter': 16, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 6480, 'label': '77760.bo.2h', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 37056122
    {'center': '36.a1', 'center_index': 36, 'center_order': 2160, 'counter': 17, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1', 'kernel_order': 2160, 'label': '77760.bo.4a', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056123
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  • id: 37056124
    {'center': '720.a1', 'center_index': 720, 'center_order': 108, 'counter': 19, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '720.763', 'image_order': 720, 'indicator': 1, 'kernel': '720.a1', 'kernel_order': 108, 'label': '77760.bo.5a', 'nt': [6, 16], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056126
    {'center': '720.a1', 'center_index': 720, 'center_order': 108, 'counter': 20, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '720.763', 'image_order': 720, 'indicator': 1, 'kernel': '720.a1', 'kernel_order': 108, 'label': '77760.bo.5b', 'nt': [6, 16], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056127
    {'center': '720.a1', 'center_index': 720, 'center_order': 108, 'counter': 21, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '720.763', 'image_order': 720, 'indicator': 1, 'kernel': '720.a1', 'kernel_order': 108, 'label': '77760.bo.5c', 'nt': [12, 183], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056128
    {'center': '720.a1', 'center_index': 720, 'center_order': 108, 'counter': 22, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '720.763', 'image_order': 720, 'indicator': 1, 'kernel': '720.a1', 'kernel_order': 108, 'label': '77760.bo.5d', 'nt': [12, 183], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056129
    {'center': '720.a1', 'center_index': 720, 'center_order': 108, 'counter': 23, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '1440.5842', 'image_order': 1440, 'indicator': 1, 'kernel': '1440.b1', 'kernel_order': 54, 'label': '77760.bo.5e', 'nt': [12, 219], 'q_character': None, 'values': [[[5, 0]], [[-5, 0]], [[-5, 0]], [[5, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-5, 0]], [[-5, 0]], [[5, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056130
    {'center': '720.a1', 'center_index': 720, 'center_order': 108, 'counter': 24, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '1440.5842', 'image_order': 1440, 'indicator': 1, 'kernel': '1440.b1', 'kernel_order': 54, 'label': '77760.bo.5f', 'nt': [12, 219], 'q_character': None, 'values': [[[5, 0]], [[-5, 0]], [[-5, 0]], [[5, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-5, 0]], [[-5, 0]], [[5, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056131
    {'center': '720.a1', 'center_index': 720, 'center_order': 108, 'counter': 25, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '1440.5842', 'image_order': 1440, 'indicator': 1, 'kernel': '1440.b1', 'kernel_order': 54, 'label': '77760.bo.5g', 'nt': [12, 219], 'q_character': None, 'values': [[[5, 0]], [[-5, 0]], [[-5, 0]], [[5, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-5, 0]], [[-5, 0]], [[5, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056132
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  • id: 37056133
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  • id: 37056134
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  • id: 37056135
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  • id: 37056137
    {'center': '720.a1', 'center_index': 720, 'center_order': 108, 'counter': 30, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '1440.5842', 'image_order': 1440, 'indicator': 1, 'kernel': '1440.a1', 'kernel_order': 54, 'label': '77760.bo.5l', 'nt': [12, 219], 'q_character': None, 'values': [[[5, 0]], [[-5, 0]], [[5, 0]], [[-5, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-5, 0]], [[5, 0]], [[-5, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056138
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  • id: 37056139
    {'center': '720.a1', 'center_index': 720, 'center_order': 108, 'counter': 32, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '1440.5842', 'image_order': 1440, 'indicator': 1, 'kernel': '1440.a1', 'kernel_order': 54, 'label': '77760.bo.5n', 'nt': [12, 219], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[-5, 0]], [[-5, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[5, 0]], [[-5, 0]], [[-5, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056140
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  • id: 37056141
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  • id: 37056142
    {'center': '108.a1', 'center_index': 108, 'center_order': 720, 'counter': 35, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '108.17', 'image_order': 108, 'indicator': 1, 'kernel': '108.a1', 'kernel_order': 720, 'label': '77760.bo.6a', 'nt': [9, 18], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 37056143
    {'center': '108.a1', 'center_index': 108, 'center_order': 720, 'counter': 36, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '108.17', 'image_order': 108, 'indicator': 1, 'kernel': '108.a1', 'kernel_order': 720, 'label': '77760.bo.6b', 'nt': [18, 51], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 37056144
    {'center': '108.a1', 'center_index': 108, 'center_order': 720, 'counter': 37, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '216.102', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1', 'kernel_order': 360, 'label': '77760.bo.6c', 'nt': [18, 94], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 37056145
    {'center': '108.a1', 'center_index': 108, 'center_order': 720, 'counter': 38, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '216.102', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1', 'kernel_order': 360, 'label': '77760.bo.6d', 'nt': [18, 94], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 37056146
    {'center': '720.a1', 'center_index': 720, 'center_order': 108, 'counter': 39, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '720.763', 'image_order': 720, 'indicator': 1, 'kernel': '720.a1', 'kernel_order': 108, 'label': '77760.bo.9a', 'nt': [10, 32], 'q_character': None, 'values': [[[9, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 37056148
    {'center': '720.a1', 'center_index': 720, 'center_order': 108, 'counter': 40, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '720.763', 'image_order': 720, 'indicator': 1, 'kernel': '720.a1', 'kernel_order': 108, 'label': '77760.bo.9b', 'nt': [20, 145], 'q_character': None, 'values': [[[9, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 37056149
    {'center': '720.a1', 'center_index': 720, 'center_order': 108, 'counter': 41, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '1440.5842', 'image_order': 1440, 'indicator': 1, 'kernel': '1440.b1', 'kernel_order': 54, 'label': '77760.bo.9c', 'nt': [20, 199], 'q_character': None, 'values': [[[9, 0]], [[-9, 0]], [[-9, 0]], [[9, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-9, 0]], [[-9, 0]], [[9, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-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: 37056150
    {'center': '720.a1', 'center_index': 720, 'center_order': 108, 'counter': 42, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '1440.5842', 'image_order': 1440, 'indicator': 1, 'kernel': '1440.b1', 'kernel_order': 54, 'label': '77760.bo.9d', 'nt': [20, 199], 'q_character': None, 'values': [[[9, 0]], [[-9, 0]], [[-9, 0]], [[9, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-9, 0]], [[-9, 0]], [[9, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[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: 37056151
    {'center': '720.a1', 'center_index': 720, 'center_order': 108, 'counter': 43, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '1440.5842', 'image_order': 1440, 'indicator': 1, 'kernel': '1440.a1', 'kernel_order': 54, 'label': '77760.bo.9e', 'nt': [20, 199], 'q_character': None, 'values': [[[9, 0]], [[-9, 0]], [[9, 0]], [[-9, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-9, 0]], [[9, 0]], [[-9, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-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: 37056152
    {'center': '720.a1', 'center_index': 720, 'center_order': 108, 'counter': 44, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '1440.5842', 'image_order': 1440, 'indicator': 1, 'kernel': '1440.a1', 'kernel_order': 54, 'label': '77760.bo.9f', 'nt': [20, 199], 'q_character': None, 'values': [[[9, 0]], [[-9, 0]], [[9, 0]], [[-9, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-9, 0]], [[9, 0]], [[-9, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[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: 37056153
    {'center': '720.a1', 'center_index': 720, 'center_order': 108, 'counter': 45, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '1440.5842', 'image_order': 1440, 'indicator': 1, 'kernel': '1440.a1', 'kernel_order': 54, 'label': '77760.bo.9g', 'nt': [20, 199], 'q_character': None, 'values': [[[9, 0]], [[9, 0]], [[-9, 0]], [[-9, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[9, 0]], [[-9, 0]], [[-9, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[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: 37056154
    {'center': '720.a1', 'center_index': 720, 'center_order': 108, 'counter': 46, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '1440.5842', 'image_order': 1440, 'indicator': 1, 'kernel': '1440.a1', 'kernel_order': 54, 'label': '77760.bo.9h', 'nt': [20, 199], 'q_character': None, 'values': [[[9, 0]], [[9, 0]], [[-9, 0]], [[-9, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[9, 0]], [[-9, 0]], [[-9, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-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: 37056155
    {'center': '4320.a1', 'center_index': 4320, 'center_order': 18, 'counter': 47, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '4320.bg', 'image_order': 4320, 'indicator': 1, 'kernel': '4320.a1', 'kernel_order': 18, 'label': '77760.bo.10a', 'nt': [18, 452], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[10, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[10, 0]], [[10, 0]], [[-5, 0]], [[-5, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[-3, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056156
    {'center': '4320.a1', 'center_index': 4320, 'center_order': 18, 'counter': 48, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '4320.bg', 'image_order': 4320, 'indicator': 1, 'kernel': '4320.a1', 'kernel_order': 18, 'label': '77760.bo.10b', 'nt': [18, 452], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[10, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[10, 0]], [[10, 0]], [[-5, 0]], [[-5, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[1, 0]], [[-3, 0]], [[2, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056157
    {'center': '4320.a1', 'center_index': 4320, 'center_order': 18, 'counter': 49, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '4320.bg', 'image_order': 4320, 'indicator': 1, 'kernel': '4320.a1', 'kernel_order': 18, 'label': '77760.bo.10c', 'nt': [18, 452], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[10, 0]], [[-5, 0]], [[10, 0]], [[-5, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-3, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-1, 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]]]}
  • id: 37056159
    {'center': '4320.a1', 'center_index': 4320, 'center_order': 18, 'counter': 50, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '4320.bg', 'image_order': 4320, 'indicator': 1, 'kernel': '4320.a1', 'kernel_order': 18, 'label': '77760.bo.10d', 'nt': [18, 452], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[10, 0]], [[-5, 0]], [[10, 0]], [[-5, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[2, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-1, 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]]]}
  • id: 37056160
    {'center': '720.a1', 'center_index': 720, 'center_order': 108, 'counter': 51, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '720.763', 'image_order': 720, 'indicator': 1, 'kernel': '720.a1', 'kernel_order': 108, 'label': '77760.bo.10e', 'nt': [30, 164], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[10, 0]], [[10, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[10, 0]], [[10, 0]], [[10, 0]], [[10, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[10, 0]], [[10, 0]], [[10, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056161
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  • id: 37056162
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  • id: 37056163
    {'center': '720.a1', 'center_index': 720, 'center_order': 108, 'counter': 54, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '1440.5842', 'image_order': 1440, 'indicator': 1, 'kernel': '1440.b1', 'kernel_order': 54, 'label': '77760.bo.10h', 'nt': [30, 261], 'q_character': None, 'values': [[[10, 0]], [[-10, 0]], [[-10, 0]], [[10, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[10, 0]], [[10, 0]], [[10, 0]], [[10, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-10, 0]], [[-10, 0]], [[10, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056164
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  • id: 37056165
    {'center': '720.a1', 'center_index': 720, 'center_order': 108, 'counter': 56, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '1440.5842', 'image_order': 1440, 'indicator': 1, 'kernel': '1440.a1', 'kernel_order': 54, 'label': '77760.bo.10j', 'nt': [30, 261], 'q_character': None, 'values': [[[10, 0]], [[-10, 0]], [[10, 0]], [[-10, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[10, 0]], [[10, 0]], [[10, 0]], [[10, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-10, 0]], [[10, 0]], [[-10, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056166
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  • id: 37056167
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  • id: 37056168
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  • id: 37056170
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  • id: 37056171
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  • id: 37056172
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  • id: 37056173
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  • id: 37056174
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  • id: 37056175
    {'center': '4320.a1', 'center_index': 4320, 'center_order': 18, 'counter': 65, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '8640.t', 'image_order': 8640, 'indicator': 1, 'kernel': '8640.a1', 'kernel_order': 9, 'label': '77760.bo.10s', 'nt': [36, 7407], 'q_character': None, 'values': [[[10, 0]], [[-10, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[10, 0]], [[-5, 0]], [[10, 0]], [[-5, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[3, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 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]]]}
  • id: 37056176
    {'center': '4320.a1', 'center_index': 4320, 'center_order': 18, 'counter': 66, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '8640.t', 'image_order': 8640, 'indicator': 1, 'kernel': '8640.a1', 'kernel_order': 9, 'label': '77760.bo.10t', 'nt': [36, 7407], 'q_character': None, 'values': [[[10, 0]], [[-10, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[10, 0]], [[-5, 0]], [[10, 0]], [[-5, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[2, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-1, 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]]]}
  • id: 37056177
    {'center': '4320.a1', 'center_index': 4320, 'center_order': 18, 'counter': 67, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '8640.t', 'image_order': 8640, 'indicator': 1, 'kernel': '8640.a1', 'kernel_order': 9, 'label': '77760.bo.10u', 'nt': [36, 7407], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[-10, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[10, 0]], [[10, 0]], [[-5, 0]], [[-5, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[-1, 0]], [[3, 0]], [[2, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056178
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  • id: 37056179
    {'center': '4320.a1', 'center_index': 4320, 'center_order': 18, 'counter': 69, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '8640.t', 'image_order': 8640, 'indicator': 1, 'kernel': '8640.a1', 'kernel_order': 9, 'label': '77760.bo.10w', 'nt': [36, 7407], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[-10, 0]], [[0, 0]], [[2, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[10, 0]], [[10, 0]], [[-5, 0]], [[-5, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[0, 0]], [[2, 0]], [[-6, 0]], [[3, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056181
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  • id: 37056182
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  • id: 37056183
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  • id: 37056184
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  • id: 37056185
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  • id: 37056186
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  • id: 37056187
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  • id: 37056188
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  • id: 37056189
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  • id: 37056190
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  • id: 37056192
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  • id: 37056193
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  • id: 37056194
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  • id: 37056195
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  • id: 37056196
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  • id: 37056197
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  • id: 37056198
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  • id: 37056199
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  • id: 37056200
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  • id: 37056201
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  • id: 37056203
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  • id: 37056204
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  • id: 37056205
    {'center': '4320.a1', 'center_index': 4320, 'center_order': 18, 'counter': 92, 'cyclotomic_n': 1, 'dim': 20, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '4320.bg', 'image_order': 4320, 'indicator': 1, 'kernel': '4320.a1', 'kernel_order': 18, 'label': '77760.bo.20j', 'nt': [90, 0], 'q_character': None, 'values': [[[20, 0]], [[0, 0]], [[20, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[20, 0]], [[20, 0]], [[-10, 0]], [[-10, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-10, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 37056206
    {'center': '4320.a1', 'center_index': 4320, 'center_order': 18, 'counter': 93, 'cyclotomic_n': 1, 'dim': 20, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '4320.bg', 'image_order': 4320, 'indicator': 1, 'kernel': '4320.a1', 'kernel_order': 18, 'label': '77760.bo.20k', 'nt': [90, 0], 'q_character': None, 'values': [[[20, 0]], [[20, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[20, 0]], [[-10, 0]], [[20, 0]], [[-10, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-10, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 37056207
    {'center': '4320.a1', 'center_index': 4320, 'center_order': 18, 'counter': 94, 'cyclotomic_n': 1, 'dim': 20, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '4320.bg', 'image_order': 4320, 'indicator': 1, 'kernel': '4320.a1', 'kernel_order': 18, 'label': '77760.bo.20l', 'nt': [90, 0], 'q_character': None, 'values': [[[20, 0]], [[20, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[20, 0]], [[-10, 0]], [[20, 0]], [[-10, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-10, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 37056208
    {'center': '77760.a1', 'center_index': 77760, 'center_order': 1, 'counter': 95, 'cyclotomic_n': 1, 'dim': 30, 'faithful': True, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '77760.bo', 'image_order': 77760, 'indicator': 1, 'kernel': '77760.a1', 'kernel_order': 1, 'label': '77760.bo.30a', 'nt': [54, 0], 'q_character': None, 'values': [[[30, 0]], [[0, 0]], [[0, 0]], [[10, 0]], [[-6, 0]], [[18, 0]], [[6, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-15, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[12, 0]], [[3, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[3, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056209
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  • id: 37056210
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  • id: 37056211
    {'center': '77760.a1', 'center_index': 77760, 'center_order': 1, 'counter': 98, 'cyclotomic_n': 1, 'dim': 30, 'faithful': True, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '77760.bo', 'image_order': 77760, 'indicator': 1, 'kernel': '77760.a1', 'kernel_order': 1, 'label': '77760.bo.30d', 'nt': [108, 0], 'q_character': None, 'values': [[[30, 0]], [[0, 0]], [[0, 0]], [[-10, 0]], [[-6, 0]], [[18, 0]], [[6, 0]], [[2, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-15, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[12, 0]], [[3, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[3, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056212
    {'center': '77760.a1', 'center_index': 77760, 'center_order': 1, 'counter': 99, 'cyclotomic_n': 1, 'dim': 30, 'faithful': True, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '77760.bo', 'image_order': 77760, 'indicator': 1, 'kernel': '77760.a1', 'kernel_order': 1, 'label': '77760.bo.30e', 'nt': [108, 0], 'q_character': None, 'values': [[[30, 0]], [[0, 0]], [[0, 0]], [[-10, 0]], [[6, 0]], [[-18, 0]], [[6, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-15, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[12, 0]], [[3, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[-3, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056094
    {'center': '77760.a1', 'center_index': 77760, 'center_order': 1, 'counter': 100, 'cyclotomic_n': 1, 'dim': 30, 'faithful': True, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '77760.bo', 'image_order': 77760, 'indicator': 1, 'kernel': '77760.a1', 'kernel_order': 1, 'label': '77760.bo.30f', 'nt': [108, 0], 'q_character': None, 'values': [[[30, 0]], [[0, 0]], [[0, 0]], [[-10, 0]], [[18, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-15, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[-9, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056095
    {'center': '77760.a1', 'center_index': 77760, 'center_order': 1, 'counter': 101, 'cyclotomic_n': 1, 'dim': 30, 'faithful': True, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '77760.bo', 'image_order': 77760, 'indicator': 1, 'kernel': '77760.a1', 'kernel_order': 1, 'label': '77760.bo.30g', 'nt': [108, 0], 'q_character': None, 'values': [[[30, 0]], [[0, 0]], [[0, 0]], [[10, 0]], [[-18, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-15, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[9, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056096
    {'center': '77760.a1', 'center_index': 77760, 'center_order': 1, 'counter': 102, 'cyclotomic_n': 1, 'dim': 30, 'faithful': True, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '77760.bo', 'image_order': 77760, 'indicator': 1, 'kernel': '77760.a1', 'kernel_order': 1, 'label': '77760.bo.30h', 'nt': [108, 0], 'q_character': None, 'values': [[[30, 0]], [[0, 0]], [[0, 0]], [[10, 0]], [[6, 0]], [[-18, 0]], [[6, 0]], [[2, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-15, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[12, 0]], [[3, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[-3, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056097
    {'center': '4320.a1', 'center_index': 4320, 'center_order': 18, 'counter': 103, 'cyclotomic_n': 1, 'dim': 32, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '4320.bg', 'image_order': 4320, 'indicator': 1, 'kernel': '4320.a1', 'kernel_order': 18, 'label': '77760.bo.32a', 'nt': [90, 0], 'q_character': None, 'values': [[[32, 0]], [[0, 0]], [[32, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[32, 0]], [[32, 0]], [[-16, 0]], [[-16, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056098
    {'center': '4320.a1', 'center_index': 4320, 'center_order': 18, 'counter': 104, 'cyclotomic_n': 1, 'dim': 32, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '4320.bg', 'image_order': 4320, 'indicator': 1, 'kernel': '4320.a1', 'kernel_order': 18, 'label': '77760.bo.32b', 'nt': [90, 0], 'q_character': None, 'values': [[[32, 0]], [[32, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[32, 0]], [[-16, 0]], [[32, 0]], [[-16, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 37056099
    {'center': '4320.a1', 'center_index': 4320, 'center_order': 18, 'counter': 105, 'cyclotomic_n': 1, 'dim': 32, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '8640.t', 'image_order': 8640, 'indicator': 1, 'kernel': '8640.a1', 'kernel_order': 9, 'label': '77760.bo.32c', 'nt': [180, 0], 'q_character': None, 'values': [[[32, 0]], [[-32, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[32, 0]], [[-16, 0]], [[32, 0]], [[-16, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]]]}
  • id: 37056100
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  • id: 37056101
    {'center': '25920.a1', 'center_index': 25920, 'center_order': 3, 'counter': 107, 'cyclotomic_n': 1, 'dim': 36, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '25920.w', 'image_order': 25920, 'indicator': 1, 'kernel': '25920.a1', 'kernel_order': 3, 'label': '77760.bo.36a', 'nt': [60, 0], 'q_character': None, 'values': [[[36, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[36, 0]], [[-18, 0]], [[-18, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[4, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056102
    {'center': '25920.a1', 'center_index': 25920, 'center_order': 3, 'counter': 108, 'cyclotomic_n': 1, 'dim': 36, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '25920.w', 'image_order': 25920, 'indicator': 1, 'kernel': '25920.a1', 'kernel_order': 3, 'label': '77760.bo.36b', 'nt': [120, 0], 'q_character': None, 'values': [[[36, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[36, 0]], [[-18, 0]], [[-18, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[6, 0]], [[6, 0]], [[4, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056103
    {'center': '25920.a1', 'center_index': 25920, 'center_order': 3, 'counter': 109, 'cyclotomic_n': 1, 'dim': 40, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '25920.w', 'image_order': 25920, 'indicator': 1, 'kernel': '25920.a1', 'kernel_order': 3, 'label': '77760.bo.40a', 'nt': [180, 0], 'q_character': None, 'values': [[[40, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[40, 0]], [[-20, 0]], [[-20, 0]], [[10, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[8, 0]], [[-4, 0]], [[4, 0]], [[-8, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056105
    {'center': '25920.a1', 'center_index': 25920, 'center_order': 3, 'counter': 110, 'cyclotomic_n': 1, 'dim': 40, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '25920.w', 'image_order': 25920, 'indicator': 1, 'kernel': '25920.a1', 'kernel_order': 3, 'label': '77760.bo.40b', 'nt': [180, 0], 'q_character': None, 'values': [[[40, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[40, 0]], [[-20, 0]], [[-20, 0]], [[10, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-8, 0]], [[4, 0]], [[-4, 0]], [[-8, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[2, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056106
    {'center': '77760.a1', 'center_index': 77760, 'center_order': 1, 'counter': 111, 'cyclotomic_n': 1, 'dim': 54, 'faithful': True, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '77760.bo', 'image_order': 77760, 'indicator': 1, 'kernel': '77760.a1', 'kernel_order': 1, 'label': '77760.bo.54a', 'nt': [90, 0], 'q_character': None, 'values': [[[54, 0]], [[0, 0]], [[0, 0]], [[18, 0]], [[18, 0]], [[18, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-27, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-9, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 37056107
    {'center': '77760.a1', 'center_index': 77760, 'center_order': 1, 'counter': 112, 'cyclotomic_n': 1, 'dim': 54, 'faithful': True, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '77760.bo', 'image_order': 77760, 'indicator': 1, 'kernel': '77760.a1', 'kernel_order': 1, 'label': '77760.bo.54b', 'nt': [180, 0], 'q_character': None, 'values': [[[54, 0]], [[0, 0]], [[0, 0]], [[-18, 0]], [[-18, 0]], [[-18, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-27, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 37056108
    {'center': '77760.a1', 'center_index': 77760, 'center_order': 1, 'counter': 113, 'cyclotomic_n': 1, 'dim': 54, 'faithful': True, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '77760.bo', 'image_order': 77760, 'indicator': 1, 'kernel': '77760.a1', 'kernel_order': 1, 'label': '77760.bo.54c', 'nt': [180, 0], 'q_character': None, 'values': [[[54, 0]], [[0, 0]], [[0, 0]], [[-18, 0]], [[18, 0]], [[18, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-27, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[9, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 37056109
    {'center': '77760.a1', 'center_index': 77760, 'center_order': 1, 'counter': 114, 'cyclotomic_n': 1, 'dim': 54, 'faithful': True, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '77760.bo', 'image_order': 77760, 'indicator': 1, 'kernel': '77760.a1', 'kernel_order': 1, 'label': '77760.bo.54d', 'nt': [180, 0], 'q_character': None, 'values': [[[54, 0]], [[0, 0]], [[0, 0]], [[18, 0]], [[-18, 0]], [[-18, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-27, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-9, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 37056110
    {'center': '77760.a1', 'center_index': 77760, 'center_order': 1, 'counter': 115, 'cyclotomic_n': 1, 'dim': 60, 'faithful': True, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '77760.bo', 'image_order': 77760, 'indicator': 1, 'kernel': '77760.a1', 'kernel_order': 1, 'label': '77760.bo.60a', 'nt': [270, 0], 'q_character': None, 'values': [[[60, 0]], [[0, 0]], [[0, 0]], [[-20, 0]], [[-12, 0]], [[12, 0]], [[-12, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-30, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[10, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 37056111
    {'center': '77760.a1', 'center_index': 77760, 'center_order': 1, 'counter': 116, 'cyclotomic_n': 1, 'dim': 60, 'faithful': True, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '77760.bo', 'image_order': 77760, 'indicator': 1, 'kernel': '77760.a1', 'kernel_order': 1, 'label': '77760.bo.60b', 'nt': [270, 0], 'q_character': None, 'values': [[[60, 0]], [[0, 0]], [[0, 0]], [[-20, 0]], [[12, 0]], [[-12, 0]], [[-12, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-30, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[10, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 37056112
    {'center': '77760.a1', 'center_index': 77760, 'center_order': 1, 'counter': 117, 'cyclotomic_n': 1, 'dim': 60, 'faithful': True, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '77760.bo', 'image_order': 77760, 'indicator': 1, 'kernel': '77760.a1', 'kernel_order': 1, 'label': '77760.bo.60c', 'nt': [270, 0], 'q_character': None, 'values': [[[60, 0]], [[0, 0]], [[0, 0]], [[20, 0]], [[-12, 0]], [[12, 0]], [[-12, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-30, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-10, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 37056113
    {'center': '77760.a1', 'center_index': 77760, 'center_order': 1, 'counter': 118, 'cyclotomic_n': 1, 'dim': 60, 'faithful': True, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '77760.bo', 'image_order': 77760, 'indicator': 1, 'kernel': '77760.a1', 'kernel_order': 1, 'label': '77760.bo.60d', 'nt': [270, 0], 'q_character': None, 'values': [[[60, 0]], [[0, 0]], [[0, 0]], [[20, 0]], [[12, 0]], [[-12, 0]], [[-12, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-30, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-10, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 37056114
    {'center': '25920.a1', 'center_index': 25920, 'center_order': 3, 'counter': 119, 'cyclotomic_n': 1, 'dim': 64, 'faithful': False, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '25920.w', 'image_order': 25920, 'indicator': 1, 'kernel': '25920.a1', 'kernel_order': 3, 'label': '77760.bo.64a', 'nt': [180, 0], 'q_character': None, 'values': [[[64, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[64, 0]], [[-32, 0]], [[-32, 0]], [[16, 0]], [[-8, 0]], [[-8, 0]], [[-8, 0]], [[-8, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37056116
    {'center': '77760.a1', 'center_index': 77760, 'center_order': 1, 'counter': 120, 'cyclotomic_n': 1, 'dim': 96, 'faithful': True, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '77760.bo', 'image_order': 77760, 'indicator': 1, 'kernel': '77760.a1', 'kernel_order': 1, 'label': '77760.bo.96a', 'nt': [270, 0], 'q_character': None, 'values': [[[96, 0]], [[0, 0]], [[0, 0]], [[32, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 37056117
    {'center': '77760.a1', 'center_index': 77760, 'center_order': 1, 'counter': 121, 'cyclotomic_n': 1, 'dim': 96, 'faithful': True, 'field': [0, 1], 'group': '77760.bo', 'group_counter': 41, 'group_order': 77760, 'image': None, 'image_isoclass': '77760.bo', 'image_order': 77760, 'indicator': 1, 'kernel': '77760.a1', 'kernel_order': 1, 'label': '77760.bo.96b', 'nt': [540, 0], 'q_character': None, 'values': [[[96, 0]], [[0, 0]], [[0, 0]], [[-32, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 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: 246054837
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 77760, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '77760.bo.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': False, 'special_labels': ['L0', 'D0', 'C0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '77760.bo', 'subgroup_hash': 4343203790838598385, 'subgroup_order': 77760, 'subgroup_tex': 'C_3^2:D_6\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246055948
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 38880, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '77760.bo.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '38880.bg', 'subgroup_hash': 31441552399977669, 'subgroup_order': 38880, 'subgroup_tex': 'C_3^2:C_6\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056909
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 38880, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '77760.bo.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '38880.bk', 'subgroup_hash': 9157942655354823479, 'subgroup_order': 38880, 'subgroup_tex': 'C_3^2:(S_3\\times S_6)', 'supersolvable': False, 'sylow': 0}
  • id: 246057020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 38880, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '77760.bo.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': False, 'special_labels': ['C1', 'C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '38880.bm', 'subgroup_hash': 6643925383203414952, 'subgroup_order': 38880, 'subgroup_tex': 'C_3^2:D_6\\times A_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057131
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 38880, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '77760.bo.2.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '38880.bf', 'subgroup_hash': 6438938557571720405, 'subgroup_order': 38880, 'subgroup_tex': 'C_3^2:S_3\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057242
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 38880, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '77760.bo.2.e1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '38880.bj', 'subgroup_hash': 1202403377994901619, 'subgroup_order': 38880, 'subgroup_tex': 'C_3^2:(S_3\\times S_6)', 'supersolvable': False, 'sylow': 0}
  • id: 246057353
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 12960, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '25920.w', 'subgroup_hash': 8300500786848619373, 'subgroup_order': 25920, 'subgroup_tex': 'S_3^2\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057464
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 19440, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '77760.bo.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '19440.bb', 'subgroup_hash': 527354253826721014, 'subgroup_order': 19440, 'subgroup_tex': 'C_3^2:C_6\\times A_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057575
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 19440, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '77760.bo.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '19440.bc', 'subgroup_hash': 1359899944358738076, 'subgroup_order': 19440, 'subgroup_tex': 'C_3^2:S_3\\times A_6', 'supersolvable': False, 'sylow': 0}
  • id: 246054838
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 19440, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '77760.bo.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '19440.bf', 'subgroup_hash': 6696393487358284414, 'subgroup_order': 19440, 'subgroup_tex': '\\He_3\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246054949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 19440, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '77760.bo.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '19440.bd', 'subgroup_hash': 1936046315932152012, 'subgroup_order': 19440, 'subgroup_tex': '\\He_3:S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246055060
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 19440, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '77760.bo.4.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '19440.be', 'subgroup_hash': 6330797916935732330, 'subgroup_order': 19440, 'subgroup_tex': '\\He_3:S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246055171
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 12960, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '77760.bo.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12960.cn', 'subgroup_hash': 1596196825562955252, 'subgroup_order': 12960, 'subgroup_tex': 'C_3:S_3\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246055282
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 6480, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, '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': '12960.bi', 'subgroup_hash': 1730392048136745174, 'subgroup_order': 12960, 'subgroup_tex': 'C_3\\times S_3\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246055393
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6480, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, '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': '12960.bj', 'subgroup_hash': 484546224911608002, 'subgroup_order': 12960, 'subgroup_tex': 'A_6:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246055504
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6480, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1', 'outer_equivalence': True, 'perfect': False, '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': '12960.bh', 'subgroup_hash': 5157357650540333956, 'subgroup_order': 12960, 'subgroup_tex': 'A_6:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246055615
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6480, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1', 'outer_equivalence': True, 'perfect': False, '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': '12960.ba', 'subgroup_hash': 1997186447382608859, 'subgroup_order': 12960, 'subgroup_tex': 'S_3^2\\times A_6', 'supersolvable': False, 'sylow': 0}
  • id: 246055726
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6.f1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1', 'outer_equivalence': True, 'perfect': False, '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': '12960.bv', 'subgroup_hash': 6297926445713512990, 'subgroup_order': 12960, 'subgroup_tex': 'C_3^2:D_6\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246055837
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 6480, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1', 'outer_equivalence': True, 'perfect': False, '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': '12960.bi', 'subgroup_hash': 1730392048136745174, 'subgroup_order': 12960, 'subgroup_tex': 'C_3\\times S_3\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246055949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 2160, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.h1', 'outer_equivalence': True, 'perfect': False, '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': '12960.bi', 'subgroup_hash': 1730392048136745174, 'subgroup_order': 12960, 'subgroup_tex': 'C_3\\times S_3\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056060
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6480, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1', 'outer_equivalence': True, 'perfect': False, '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': '12960.bj', 'subgroup_hash': 484546224911608002, 'subgroup_order': 12960, 'subgroup_tex': 'A_6:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246056171
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 9720, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '77760.bo.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': False, 'special_labels': ['D', 'L1', 'D1', 'D', 'L1', 'D1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9720.bc', 'subgroup_hash': 1073483167708412023, 'subgroup_order': 9720, 'subgroup_tex': '\\He_3\\times A_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056282
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 720, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8640.t', 'subgroup_hash': 1113057395295209127, 'subgroup_order': 8640, 'subgroup_tex': 'D_6\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056393
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2160, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8640.t', 'subgroup_hash': 1113057395295209127, 'subgroup_order': 8640, 'subgroup_tex': 'D_6\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056504
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.10.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '7776.is', 'subgroup_hash': 4994213685505676867, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4:(D_4\\times D_6)', 'supersolvable': False, 'sylow': 0}
  • id: 246056615
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6480, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '77760.bo.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6480.dh', 'subgroup_hash': 2241263590585653093, 'subgroup_order': 6480, 'subgroup_tex': 'C_3:S_3\\times A_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056726
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 6480, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '77760.bo.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6480.df', 'subgroup_hash': 5505678841158151309, 'subgroup_order': 6480, 'subgroup_tex': 'C_3^2\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056837
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6480, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '77760.bo.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6480.dg', 'subgroup_hash': 9007943657742285918, 'subgroup_order': 6480, 'subgroup_tex': 'C_3^2:S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056898
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3240, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, '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': '6480.bp', 'subgroup_hash': 1259049183565800588, 'subgroup_order': 6480, 'subgroup_tex': 'C_3\\times S_3\\times A_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056910
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1', 'outer_equivalence': True, 'perfect': False, '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': '6480.cl', 'subgroup_hash': 3432543176310741949, 'subgroup_order': 6480, 'subgroup_tex': 'C_3^2:C_6\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246056921
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1', 'outer_equivalence': True, 'perfect': False, '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': '6480.cj', 'subgroup_hash': 1236312392635462969, 'subgroup_order': 6480, 'subgroup_tex': '\\GL(2,4).S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246056932
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1', 'outer_equivalence': True, 'perfect': False, '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': '6480.ck', 'subgroup_hash': 4793595070712656675, 'subgroup_order': 6480, 'subgroup_tex': '\\GL(2,4).S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246056943
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3240, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1', 'outer_equivalence': True, 'perfect': False, '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': '6480.bp', 'subgroup_hash': 1259049183565800588, 'subgroup_order': 6480, 'subgroup_tex': 'C_3\\times S_3\\times A_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056954
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1080, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1', 'outer_equivalence': True, 'perfect': False, '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': '6480.bp', 'subgroup_hash': 1259049183565800588, 'subgroup_order': 6480, 'subgroup_tex': 'C_3\\times S_3\\times A_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056965
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 54, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1', 'outer_equivalence': True, 'perfect': False, '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': '6480.cn', 'subgroup_hash': 4455483148384328705, 'subgroup_order': 6480, 'subgroup_tex': 'C_3^2:S_3\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246056976
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1', 'outer_equivalence': True, 'perfect': False, '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': '6480.cm', 'subgroup_hash': 716388572407914505, 'subgroup_order': 6480, 'subgroup_tex': '\\GL(2,4).S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246056987
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 2160, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.l1', 'outer_equivalence': True, 'perfect': False, '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': '6480.df', 'subgroup_hash': 5505678841158151309, 'subgroup_order': 6480, 'subgroup_tex': 'C_3^2\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056998
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3240, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1', 'outer_equivalence': True, 'perfect': False, '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': '6480.bv', 'subgroup_hash': 2295876809505866224, 'subgroup_order': 6480, 'subgroup_tex': 'C_3^2:S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057009
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3240, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.n1', 'outer_equivalence': True, 'perfect': False, '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': '6480.bv', 'subgroup_hash': 2295876809505866224, 'subgroup_order': 6480, 'subgroup_tex': 'C_3^2:S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1080, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.o1', 'outer_equivalence': True, 'perfect': False, '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': '6480.bv', 'subgroup_hash': 2295876809505866224, 'subgroup_order': 6480, 'subgroup_tex': 'C_3^2:S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057032
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 108, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.15.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5184.pk', 'subgroup_hash': 1020202082189047288, 'subgroup_order': 5184, 'subgroup_tex': 'C_6^2:D_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057043
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 720, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4320.bt', 'subgroup_hash': 6716676110426446033, 'subgroup_order': 4320, 'subgroup_tex': 'C_6\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 360, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.18.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4320.bv', 'subgroup_hash': 3755218601515265701, 'subgroup_order': 4320, 'subgroup_tex': 'C_6:S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057065
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2160, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.18.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4320.bg', 'subgroup_hash': 8915526446794886175, 'subgroup_order': 4320, 'subgroup_tex': 'S_3\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057076
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 720, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.18.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4320.bg', 'subgroup_hash': 8915526446794886175, 'subgroup_order': 4320, 'subgroup_tex': 'S_3\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057087
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 360, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.18.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4320.bg', 'subgroup_hash': 8915526446794886175, 'subgroup_order': 4320, 'subgroup_tex': 'S_3\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057098
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1080, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.18.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4320.bg', 'subgroup_hash': 8915526446794886175, 'subgroup_order': 4320, 'subgroup_tex': 'S_3\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057109
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 360, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.18.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4320.bu', 'subgroup_hash': 4485744617830973288, 'subgroup_order': 4320, 'subgroup_tex': 'D_6\\times A_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057120
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1080, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.18.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4320.bu', 'subgroup_hash': 4485744617830973288, 'subgroup_order': 4320, 'subgroup_tex': 'D_6\\times A_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057132
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.18.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4320.bp', 'subgroup_hash': 3016394576679025638, 'subgroup_order': 4320, 'subgroup_tex': 'S_3^2\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057143
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2160, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.18.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4320.bt', 'subgroup_hash': 6716676110426446033, 'subgroup_order': 4320, 'subgroup_tex': 'C_6\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057154
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1080, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.18.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4320.bv', 'subgroup_hash': 3755218601515265701, 'subgroup_order': 4320, 'subgroup_tex': 'C_6:S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057165
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 720, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.18.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4320.bg', 'subgroup_hash': 8915526446794886175, 'subgroup_order': 4320, 'subgroup_tex': 'S_3\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057176
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 720, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.18.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4320.bg', 'subgroup_hash': 8915526446794886175, 'subgroup_order': 4320, 'subgroup_tex': 'S_3\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057187
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 360, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.18.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4320.bg', 'subgroup_hash': 8915526446794886175, 'subgroup_order': 4320, 'subgroup_tex': 'S_3\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057198
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.20.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.in', 'subgroup_hash': 8680384176493874130, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^4:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 246057209
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.20.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.io', 'subgroup_hash': 8832992903767141139, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^4:(C_6\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 246057220
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.20.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.im', 'subgroup_hash': 3432053452636570107, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^4:(C_2\\times D_{12})', 'supersolvable': False, 'sylow': 0}
  • id: 246057231
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.20.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.ik', 'subgroup_hash': 604697750936728859, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057243
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.20.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.il', 'subgroup_hash': 5553770281982022740, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^4:(C_4\\times D_6)', 'supersolvable': False, 'sylow': 0}
  • id: 246057254
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.20.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.ir', 'subgroup_hash': 781723869134371487, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^4:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 246057265
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 54, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.20.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.iq', 'subgroup_hash': 3474855449679596549, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^4:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 246057276
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.20.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.it', 'subgroup_hash': 3026284031104468230, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^4:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 246057287
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3240, 'counter': 64, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '77760.bo.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3240.cl', 'subgroup_hash': 4896948197276926329, 'subgroup_order': 3240, 'subgroup_tex': 'C_3^2\\times A_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057298
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3240.bw', 'subgroup_hash': 4706353329828722467, 'subgroup_order': 3240, 'subgroup_tex': 'C_3^2:C_6\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057309
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 54, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3240.cb', 'subgroup_hash': 476223097382468647, 'subgroup_order': 3240, 'subgroup_tex': 'C_3^2:S_3\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057320
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.24.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3240.cc', 'subgroup_hash': 8764120736652342740, 'subgroup_order': 3240, 'subgroup_tex': '\\He_3\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057331
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.24.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3240.bx', 'subgroup_hash': 4478716364388308090, 'subgroup_order': 3240, 'subgroup_tex': '\\He_3:S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057342
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.24.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3240.bz', 'subgroup_hash': 7949543960855971593, 'subgroup_order': 3240, 'subgroup_tex': '\\He_3:S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057354
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1080, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.24.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3240.cl', 'subgroup_hash': 4896948197276926329, 'subgroup_order': 3240, 'subgroup_tex': 'C_3^2\\times A_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057365
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 720, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.27.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2880.du', 'subgroup_hash': 7330512212170881535, 'subgroup_order': 2880, 'subgroup_tex': 'C_2^2\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057376
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.30.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.a1', 'outer_equivalence': True, 'perfect': False, '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': '2592.mq', 'subgroup_hash': 9167354683707208537, 'subgroup_order': 2592, 'subgroup_tex': 'C_2\\times C_6^2:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057387
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.30.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.b1', 'outer_equivalence': True, 'perfect': False, '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': '2592.lc', 'subgroup_hash': 8934809208614015284, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^2:D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057398
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.30.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.c1', 'outer_equivalence': True, 'perfect': False, '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': '2592.mp', 'subgroup_hash': 3980713857547859626, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^2:D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057409
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.30.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.d1', 'outer_equivalence': True, 'perfect': False, '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': '2592.lc', 'subgroup_hash': 8934809208614015284, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^2:D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057420
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.30.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.e1', 'outer_equivalence': True, 'perfect': False, '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': '2592.fs', 'subgroup_hash': 3641402233686599739, 'subgroup_order': 2592, 'subgroup_tex': 'S_3^4:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 246057431
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 108, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.30.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.f1', 'outer_equivalence': True, 'perfect': False, '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': '2592.mo', 'subgroup_hash': 1076202657384780556, 'subgroup_order': 2592, 'subgroup_tex': 'C_6^2:(C_6\\times D_6)', 'supersolvable': False, 'sylow': 0}
  • id: 246057442
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 108, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.30.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.g1', 'outer_equivalence': True, 'perfect': False, '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': '2592.lc', 'subgroup_hash': 8934809208614015284, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^2:D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057453
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 108, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.30.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.h1', 'outer_equivalence': True, 'perfect': False, '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': '2592.lc', 'subgroup_hash': 8934809208614015284, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^2:D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057465
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.30.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.i1', 'outer_equivalence': True, 'perfect': False, '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': '2592.pn', 'subgroup_hash': 5023455245458789962, 'subgroup_order': 2592, 'subgroup_tex': 'C_2\\times C_6^2:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057476
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.30.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.j1', 'outer_equivalence': True, 'perfect': False, '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': '2592.lc', 'subgroup_hash': 8934809208614015284, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^2:D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057487
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.30.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.k1', 'outer_equivalence': True, 'perfect': False, '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': '2592.od', 'subgroup_hash': 8913694849733206168, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^2:D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057498
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.30.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.l1', 'outer_equivalence': True, 'perfect': False, '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': '2592.lc', 'subgroup_hash': 8934809208614015284, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^2:D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057509
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 2160, 'counter': 84, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '77760.bo.36.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2160.bz', 'subgroup_hash': 7467210928949091379, 'subgroup_order': 2160, 'subgroup_tex': 'C_3\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057520
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 360, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.36.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.cn', 'subgroup_hash': 1243875770078870382, 'subgroup_order': 2160, 'subgroup_tex': 'C_6\\times A_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057531
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.36.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.ce', 'subgroup_hash': 7514770946210304289, 'subgroup_order': 2160, 'subgroup_tex': '\\GL(2,4):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057542
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.36.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.ci', 'subgroup_hash': 1774093765926653042, 'subgroup_order': 2160, 'subgroup_tex': 'A_5:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057553
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1080, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.36.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.ca', 'subgroup_hash': 4260759077021065075, 'subgroup_order': 2160, 'subgroup_tex': 'S_3\\times A_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057564
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 360, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.36.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.ca', 'subgroup_hash': 4260759077021065075, 'subgroup_order': 2160, 'subgroup_tex': 'S_3\\times A_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057576
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.36.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.ct', 'subgroup_hash': 303238497438261444, 'subgroup_order': 2160, 'subgroup_tex': '\\GL(2,4):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057587
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.36.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.ch', 'subgroup_hash': 4798984224298730333, 'subgroup_order': 2160, 'subgroup_tex': 'A_5:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057598
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.36.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.cm', 'subgroup_hash': 6018971842015229741, 'subgroup_order': 2160, 'subgroup_tex': 'S_3^2\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057609
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.36.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1', 'outer_equivalence': True, 'perfect': False, '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': '2160.cr', 'subgroup_hash': 9021572224343232945, 'subgroup_order': 2160, 'subgroup_tex': 'C_3^2:D_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246057620
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1080, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.36.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.cn', 'subgroup_hash': 1243875770078870382, 'subgroup_order': 2160, 'subgroup_tex': 'C_6\\times A_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057631
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.36.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.ce', 'subgroup_hash': 7514770946210304289, 'subgroup_order': 2160, 'subgroup_tex': '\\GL(2,4):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057642
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.36.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.ce', 'subgroup_hash': 7514770946210304289, 'subgroup_order': 2160, 'subgroup_tex': '\\GL(2,4):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057653
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.36.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.ci', 'subgroup_hash': 1774093765926653042, 'subgroup_order': 2160, 'subgroup_tex': 'A_5:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057664
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 360, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.36.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.ca', 'subgroup_hash': 4260759077021065075, 'subgroup_order': 2160, 'subgroup_tex': 'S_3\\times A_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057675
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 360, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.36.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.ca', 'subgroup_hash': 4260759077021065075, 'subgroup_order': 2160, 'subgroup_tex': 'S_3\\times A_6', 'supersolvable': False, 'sylow': 0}
  • id: 246054839
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 720, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.36.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.bz', 'subgroup_hash': 7467210928949091379, 'subgroup_order': 2160, 'subgroup_tex': 'C_3\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246054850
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 720, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.36.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.bz', 'subgroup_hash': 7467210928949091379, 'subgroup_order': 2160, 'subgroup_tex': 'C_3\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246054861
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 360, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.36.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.bz', 'subgroup_hash': 7467210928949091379, 'subgroup_order': 2160, 'subgroup_tex': 'C_3\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246054872
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1080, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.36.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.cb', 'subgroup_hash': 7557667965369541876, 'subgroup_order': 2160, 'subgroup_tex': 'C_3:S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246054883
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 360, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.36.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.cb', 'subgroup_hash': 7557667965369541876, 'subgroup_order': 2160, 'subgroup_tex': 'C_3:S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246054894
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1080, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.36.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.bz', 'subgroup_hash': 7467210928949091379, 'subgroup_order': 2160, 'subgroup_tex': 'C_3\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246054905
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 360, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.36.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.cb', 'subgroup_hash': 7557667965369541876, 'subgroup_order': 2160, 'subgroup_tex': 'C_3:S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246054916
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 360, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.36.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.cb', 'subgroup_hash': 7557667965369541876, 'subgroup_order': 2160, 'subgroup_tex': 'C_3:S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246054927
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.40.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3569', 'subgroup_hash': 3569, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246054938
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.40.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3564', 'subgroup_hash': 3564, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246054950
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.40.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3575', 'subgroup_hash': 3575, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246054961
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.40.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3482', 'subgroup_hash': 3482, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:(C_2\\times C_{12})', 'supersolvable': False, 'sylow': 0}
  • id: 246054972
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.40.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3488', 'subgroup_hash': 3488, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 246054983
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 108, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.40.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3565', 'subgroup_hash': 3565, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246054994
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.40.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3570', 'subgroup_hash': 3570, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246055005
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.40.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3574', 'subgroup_hash': 3574, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246055016
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 54, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.40.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3571', 'subgroup_hash': 3571, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246055027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.40.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3578', 'subgroup_hash': 3578, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246055038
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 54, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.40.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3491', 'subgroup_hash': 3491, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 246055049
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.40.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3495', 'subgroup_hash': 3495, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 246055061
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.40.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3507', 'subgroup_hash': 3507, 'subgroup_order': 1944, 'subgroup_tex': '\\He_3:\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 246055072
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.40.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3519', 'subgroup_hash': 3519, 'subgroup_order': 1944, 'subgroup_tex': '\\He_3:\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 246055083
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.40.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3502', 'subgroup_hash': 3502, 'subgroup_order': 1944, 'subgroup_tex': '\\He_3\\times \\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 246055094
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.40.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3527', 'subgroup_hash': 3527, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246055105
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.40.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3511', 'subgroup_hash': 3511, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246055116
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.40.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3521', 'subgroup_hash': 3521, 'subgroup_order': 1944, 'subgroup_tex': '\\He_3:\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 246055127
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.40.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3531', 'subgroup_hash': 3531, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246055138
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.45.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '45.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 45, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47874', 'subgroup_hash': 47874, 'subgroup_order': 1728, 'subgroup_tex': 'A_4:D_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 246055149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.45.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '45.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 45, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.30804', 'subgroup_hash': 30804, 'subgroup_order': 1728, 'subgroup_tex': 'C_{12}.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055160
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.48.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1620.263', 'subgroup_hash': 263, 'subgroup_order': 1620, 'subgroup_tex': '\\He_3\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 246055172
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 720, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.54.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1440.5842', 'subgroup_hash': 5842, 'subgroup_order': 1440, 'subgroup_tex': 'C_2\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246055183
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 360, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.54.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1440.5842', 'subgroup_hash': 5842, 'subgroup_order': 1440, 'subgroup_tex': 'C_2\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246055194
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 360, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.54.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1440.5845', 'subgroup_hash': 5845, 'subgroup_order': 1440, 'subgroup_tex': 'C_2^2\\times A_6', 'supersolvable': False, 'sylow': 0}
  • id: 246055205
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.54.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1440.5849', 'subgroup_hash': 5849, 'subgroup_order': 1440, 'subgroup_tex': 'D_6\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246055216
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.54.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1440.5849', 'subgroup_hash': 5849, 'subgroup_order': 1440, 'subgroup_tex': 'D_6\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246055227
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 720, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.54.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1440.5842', 'subgroup_hash': 5842, 'subgroup_order': 1440, 'subgroup_tex': 'C_2\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246055238
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 360, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.54.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1440.5842', 'subgroup_hash': 5842, 'subgroup_order': 1440, 'subgroup_tex': 'C_2\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246055249
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.a1', 'outer_equivalence': True, 'perfect': False, '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': '1296.3526', 'subgroup_hash': 3526, 'subgroup_order': 1296, 'subgroup_tex': 'S_3^3:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 246055260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.b1', 'outer_equivalence': True, 'perfect': False, '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': '1296.3525', 'subgroup_hash': 3525, 'subgroup_order': 1296, 'subgroup_tex': 'S_3^3:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246055271
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.c1', 'outer_equivalence': True, 'perfect': False, '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': '1296.3529', 'subgroup_hash': 3529, 'subgroup_order': 1296, 'subgroup_tex': 'S_3\\times C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246055283
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.d1', 'outer_equivalence': True, 'perfect': False, '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': '1296.3012', 'subgroup_hash': 3012, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2:C_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 246055294
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.e1', 'outer_equivalence': True, 'perfect': False, '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': '1296.2919', 'subgroup_hash': 2919, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246055305
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.f1', 'outer_equivalence': True, 'perfect': False, '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': '1296.3528', 'subgroup_hash': 3528, 'subgroup_order': 1296, 'subgroup_tex': 'S_3^2:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246055316
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.g1', 'outer_equivalence': True, 'perfect': False, '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': '1296.3527', 'subgroup_hash': 3527, 'subgroup_order': 1296, 'subgroup_tex': '(C_3\\times S_3^2):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246055327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.h1', 'outer_equivalence': True, 'perfect': False, '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': '1296.2943', 'subgroup_hash': 2943, 'subgroup_order': 1296, 'subgroup_tex': 'A_4\\times C_3^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246055338
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.i1', 'outer_equivalence': True, 'perfect': False, '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': '1296.2931', 'subgroup_hash': 2931, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246055349
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.j1', 'outer_equivalence': True, 'perfect': False, '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': '1296.2931', 'subgroup_hash': 2931, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246055360
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.k1', 'outer_equivalence': True, 'perfect': False, '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': '1296.3530', 'subgroup_hash': 3530, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^3:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 246055371
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.l1', 'outer_equivalence': True, 'perfect': False, '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': '1296.2919', 'subgroup_hash': 2919, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246055382
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.m1', 'outer_equivalence': True, 'perfect': False, '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': '1296.3538', 'subgroup_hash': 3538, 'subgroup_order': 1296, 'subgroup_tex': 'S_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 246055394
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.n1', 'outer_equivalence': True, 'perfect': False, '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': '1296.3524', 'subgroup_hash': 3524, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246055405
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 108, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.o1', 'outer_equivalence': True, 'perfect': False, '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': '1296.2985', 'subgroup_hash': 2985, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055416
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 108, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.p1', 'outer_equivalence': True, 'perfect': False, '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': '1296.2943', 'subgroup_hash': 2943, 'subgroup_order': 1296, 'subgroup_tex': 'A_4\\times C_3^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246055427
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.q1', 'outer_equivalence': True, 'perfect': False, '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': '1296.3526', 'subgroup_hash': 3526, 'subgroup_order': 1296, 'subgroup_tex': 'S_3^3:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 246055438
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.r1', 'outer_equivalence': True, 'perfect': False, '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': '1296.3525', 'subgroup_hash': 3525, 'subgroup_order': 1296, 'subgroup_tex': 'S_3^3:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246055449
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.s1', 'outer_equivalence': True, 'perfect': False, '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': '1296.3525', 'subgroup_hash': 3525, 'subgroup_order': 1296, 'subgroup_tex': 'S_3^3:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246055460
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.t1', 'outer_equivalence': True, 'perfect': False, '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': '1296.3529', 'subgroup_hash': 3529, 'subgroup_order': 1296, 'subgroup_tex': 'S_3\\times C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246055471
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.u1', 'outer_equivalence': True, 'perfect': False, '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': '1296.3022', 'subgroup_hash': 3022, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:D_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055482
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.v1', 'outer_equivalence': True, 'perfect': False, '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': '1296.2926', 'subgroup_hash': 2926, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246055493
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.w1', 'outer_equivalence': True, 'perfect': False, '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': '1296.2943', 'subgroup_hash': 2943, 'subgroup_order': 1296, 'subgroup_tex': 'A_4\\times C_3^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246055505
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.x1', 'outer_equivalence': True, 'perfect': False, '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': '1296.2938', 'subgroup_hash': 2938, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246055516
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.y1', 'outer_equivalence': True, 'perfect': False, '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': '1296.2938', 'subgroup_hash': 2938, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246055527
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.z1', 'outer_equivalence': True, 'perfect': False, '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': '1296.2926', 'subgroup_hash': 2926, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246055538
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.ba1', 'outer_equivalence': True, 'perfect': False, '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': '1296.2997', 'subgroup_hash': 2997, 'subgroup_order': 1296, 'subgroup_tex': 'C_2\\times \\He_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055549
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bb1', 'outer_equivalence': True, 'perfect': False, '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': '1296.3005', 'subgroup_hash': 3005, 'subgroup_order': 1296, 'subgroup_tex': 'C_2\\times \\He_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055560
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bc1', 'outer_equivalence': True, 'perfect': False, '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': '1296.2919', 'subgroup_hash': 2919, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246055571
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bd1', 'outer_equivalence': True, 'perfect': False, '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': '1296.2926', 'subgroup_hash': 2926, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246055582
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.be1', 'outer_equivalence': True, 'perfect': False, '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': '1296.2987', 'subgroup_hash': 2987, 'subgroup_order': 1296, 'subgroup_tex': 'C_2\\times S_4\\times \\He_3', 'supersolvable': False, 'sylow': 0}
  • id: 246055593
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bf1', 'outer_equivalence': True, 'perfect': False, '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': '1296.2931', 'subgroup_hash': 2931, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246055604
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bg1', 'outer_equivalence': True, 'perfect': False, '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': '1296.2938', 'subgroup_hash': 2938, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246055616
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bh1', 'outer_equivalence': True, 'perfect': False, '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': '1296.2931', 'subgroup_hash': 2931, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246055627
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bi1', 'outer_equivalence': True, 'perfect': False, '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': '1296.2919', 'subgroup_hash': 2919, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246055638
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.60.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bj1', 'outer_equivalence': True, 'perfect': False, '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': '1296.2926', 'subgroup_hash': 2926, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246055649
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 1080, 'counter': 173, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '77760.bo.72.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': False, 'special_labels': ['S', 'D2', 'S', 'D2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1080.487', 'subgroup_hash': 487, 'subgroup_order': 1080, 'subgroup_tex': 'C_3\\times A_6', 'supersolvable': False, 'sylow': 0}
  • id: 246055660
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.72.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1080.492', 'subgroup_hash': 492, 'subgroup_order': 1080, 'subgroup_tex': 'S_3\\times \\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 246055671
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.72.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.c1', 'outer_equivalence': True, 'perfect': False, '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': '1080.270', 'subgroup_hash': 270, 'subgroup_order': 1080, 'subgroup_tex': 'C_3^2:C_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246055682
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.72.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.d1', 'outer_equivalence': True, 'perfect': False, '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': '1080.276', 'subgroup_hash': 276, 'subgroup_order': 1080, 'subgroup_tex': 'C_3^2:(S_3\\times F_5)', 'supersolvable': True, 'sylow': 0}
  • id: 246055693
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.72.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1080.491', 'subgroup_hash': 491, 'subgroup_order': 1080, 'subgroup_tex': '\\GL(2,4):S_3', 'supersolvable': False, 'sylow': 0}
  • id: 246055704
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.72.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.f1', 'outer_equivalence': True, 'perfect': False, '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': '1080.287', 'subgroup_hash': 287, 'subgroup_order': 1080, 'subgroup_tex': 'D_5\\times C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055715
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.72.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1080.492', 'subgroup_hash': 492, 'subgroup_order': 1080, 'subgroup_tex': 'S_3\\times \\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 246055727
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.72.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1080.492', 'subgroup_hash': 492, 'subgroup_order': 1080, 'subgroup_tex': 'S_3\\times \\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 246055738
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 54, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.72.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.i1', 'outer_equivalence': True, 'perfect': False, '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': '1080.273', 'subgroup_hash': 273, 'subgroup_order': 1080, 'subgroup_tex': 'C_3^2:S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246055749
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.72.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.j1', 'outer_equivalence': True, 'perfect': False, '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': '1080.278', 'subgroup_hash': 278, 'subgroup_order': 1080, 'subgroup_tex': 'C_3^2:(S_3\\times F_5)', 'supersolvable': True, 'sylow': 0}
  • id: 246055760
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.72.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1080.490', 'subgroup_hash': 490, 'subgroup_order': 1080, 'subgroup_tex': 'C_3^2\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246055771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.72.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1080.490', 'subgroup_hash': 490, 'subgroup_order': 1080, 'subgroup_tex': 'C_3^2\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246055782
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.72.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1080.489', 'subgroup_hash': 489, 'subgroup_order': 1080, 'subgroup_tex': 'C_3^2:S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246055793
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.72.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1080.488', 'subgroup_hash': 488, 'subgroup_order': 1080, 'subgroup_tex': 'C_3^2:S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246055804
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.72.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1080.489', 'subgroup_hash': 489, 'subgroup_order': 1080, 'subgroup_tex': 'C_3^2:S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246055815
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.72.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1080.489', 'subgroup_hash': 489, 'subgroup_order': 1080, 'subgroup_tex': 'C_3^2:S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246055826
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 360, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.72.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1080.487', 'subgroup_hash': 487, 'subgroup_order': 1080, 'subgroup_tex': 'C_3\\times A_6', 'supersolvable': False, 'sylow': 0}
  • id: 246055838
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 360, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.72.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1080.487', 'subgroup_hash': 487, 'subgroup_order': 1080, 'subgroup_tex': 'C_3\\times A_6', 'supersolvable': False, 'sylow': 0}
  • id: 246055849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 54, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.80.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.780', 'subgroup_hash': 780, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055860
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.80.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.788', 'subgroup_hash': 788, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055871
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 54, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.80.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.790', 'subgroup_hash': 790, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.80.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.806', 'subgroup_hash': 806, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055893
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 108, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.80.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.781', 'subgroup_hash': 781, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055904
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 54, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.80.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.791', 'subgroup_hash': 791, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055915
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 54, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.80.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.810', 'subgroup_hash': 810, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055926
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 54, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.80.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.799', 'subgroup_hash': 799, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055937
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.80.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.816', 'subgroup_hash': 816, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055950
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.80.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.789', 'subgroup_hash': 789, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055961
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.80.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.807', 'subgroup_hash': 807, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055972
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.80.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.782', 'subgroup_hash': 782, 'subgroup_order': 972, 'subgroup_tex': '\\He_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055983
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.80.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.798', 'subgroup_hash': 798, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055994
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.80.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.817', 'subgroup_hash': 817, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056005
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.80.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.760', 'subgroup_hash': 760, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246056016
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.80.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.772', 'subgroup_hash': 772, 'subgroup_order': 972, 'subgroup_tex': '(C_3^2\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.80.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.767', 'subgroup_hash': 767, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246056038
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.80.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.815', 'subgroup_hash': 815, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056049
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.80.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.809', 'subgroup_hash': 809, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056061
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.a1', 'outer_equivalence': True, 'perfect': False, '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': '864.4692', 'subgroup_hash': 4692, 'subgroup_order': 864, 'subgroup_tex': 'S_3\\times C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056072
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.b1', 'outer_equivalence': True, 'perfect': False, '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': '864.4673', 'subgroup_hash': 4673, 'subgroup_order': 864, 'subgroup_tex': 'S_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246056083
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.c1', 'outer_equivalence': True, 'perfect': False, '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': '864.4690', 'subgroup_hash': 4690, 'subgroup_order': 864, 'subgroup_tex': 'C_6\\times S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056094
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.d1', 'outer_equivalence': True, 'perfect': False, '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': '864.4673', 'subgroup_hash': 4673, 'subgroup_order': 864, 'subgroup_tex': 'S_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246056105
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.e1', 'outer_equivalence': True, 'perfect': False, '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': '864.4686', 'subgroup_hash': 4686, 'subgroup_order': 864, 'subgroup_tex': 'S_3^3:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 246056116
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.f1', 'outer_equivalence': True, 'perfect': False, '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': '864.4686', 'subgroup_hash': 4686, 'subgroup_order': 864, 'subgroup_tex': 'S_3^3:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 246056127
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.g1', 'outer_equivalence': True, 'perfect': False, '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': '864.2455', 'subgroup_hash': 2455, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056138
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.h1', 'outer_equivalence': True, 'perfect': False, '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': '864.2470', 'subgroup_hash': 2470, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.i1', 'outer_equivalence': True, 'perfect': False, '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': '864.2470', 'subgroup_hash': 2470, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056160
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.j1', 'outer_equivalence': True, 'perfect': False, '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': '864.4693', 'subgroup_hash': 4693, 'subgroup_order': 864, 'subgroup_tex': 'C_2\\times A_4:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246056172
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.k1', 'outer_equivalence': True, 'perfect': False, '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': '864.4000', 'subgroup_hash': 4000, 'subgroup_order': 864, 'subgroup_tex': 'C_2\\times C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056183
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.l1', 'outer_equivalence': True, 'perfect': False, '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': '864.2510', 'subgroup_hash': 2510, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056194
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.m1', 'outer_equivalence': True, 'perfect': False, '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': '864.4673', 'subgroup_hash': 4673, 'subgroup_order': 864, 'subgroup_tex': 'S_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246056205
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.n1', 'outer_equivalence': True, 'perfect': False, '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': '864.2580', 'subgroup_hash': 2580, 'subgroup_order': 864, 'subgroup_tex': 'C_2\\times C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056216
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.o1', 'outer_equivalence': True, 'perfect': False, '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': '864.4691', 'subgroup_hash': 4691, 'subgroup_order': 864, 'subgroup_tex': 'C_6:S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056227
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.p1', 'outer_equivalence': True, 'perfect': False, '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': '864.2470', 'subgroup_hash': 2470, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056238
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.q1', 'outer_equivalence': True, 'perfect': False, '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': '864.4673', 'subgroup_hash': 4673, 'subgroup_order': 864, 'subgroup_tex': 'S_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246056249
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.r1', 'outer_equivalence': True, 'perfect': False, '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': '864.4694', 'subgroup_hash': 4694, 'subgroup_order': 864, 'subgroup_tex': 'D_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.s1', 'outer_equivalence': True, 'perfect': False, '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': '864.4673', 'subgroup_hash': 4673, 'subgroup_order': 864, 'subgroup_tex': 'S_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246056271
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.t1', 'outer_equivalence': True, 'perfect': False, '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': '864.4673', 'subgroup_hash': 4673, 'subgroup_order': 864, 'subgroup_tex': 'S_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246056283
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 108, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.u1', 'outer_equivalence': True, 'perfect': False, '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': '864.2454', 'subgroup_hash': 2454, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056294
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.v1', 'outer_equivalence': True, 'perfect': False, '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': '864.2470', 'subgroup_hash': 2470, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056305
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.w1', 'outer_equivalence': True, 'perfect': False, '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': '864.2470', 'subgroup_hash': 2470, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056316
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 108, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.x1', 'outer_equivalence': True, 'perfect': False, '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': '864.4033', 'subgroup_hash': 4033, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.y1', 'outer_equivalence': True, 'perfect': False, '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': '864.2470', 'subgroup_hash': 2470, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056338
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.z1', 'outer_equivalence': True, 'perfect': False, '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': '864.4692', 'subgroup_hash': 4692, 'subgroup_order': 864, 'subgroup_tex': 'S_3\\times C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056349
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.ba1', 'outer_equivalence': True, 'perfect': False, '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': '864.4673', 'subgroup_hash': 4673, 'subgroup_order': 864, 'subgroup_tex': 'S_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246056360
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.bb1', 'outer_equivalence': True, 'perfect': False, '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': '864.4690', 'subgroup_hash': 4690, 'subgroup_order': 864, 'subgroup_tex': 'C_6\\times S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056371
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.bc1', 'outer_equivalence': True, 'perfect': False, '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': '864.4690', 'subgroup_hash': 4690, 'subgroup_order': 864, 'subgroup_tex': 'C_6\\times S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056382
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.bd1', 'outer_equivalence': True, 'perfect': False, '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': '864.4673', 'subgroup_hash': 4673, 'subgroup_order': 864, 'subgroup_tex': 'S_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246056394
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.be1', 'outer_equivalence': True, 'perfect': False, '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': '864.2456', 'subgroup_hash': 2456, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056405
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.bf1', 'outer_equivalence': True, 'perfect': False, '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': '864.2470', 'subgroup_hash': 2470, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056416
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.bg1', 'outer_equivalence': True, 'perfect': False, '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': '864.2470', 'subgroup_hash': 2470, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056427
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.bh1', 'outer_equivalence': True, 'perfect': False, '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': '864.2511', 'subgroup_hash': 2511, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056438
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 54, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.bi1', 'outer_equivalence': True, 'perfect': False, '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': '864.2629', 'subgroup_hash': 2629, 'subgroup_order': 864, 'subgroup_tex': 'C_2\\times C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056449
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.90.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.bj1', 'outer_equivalence': True, 'perfect': False, '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': '864.2470', 'subgroup_hash': 2470, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056460
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': True, 'centralizer_order': 108, 'characteristic': True, 'core_order': 720, 'counter': 246, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '77760.bo.108.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '108.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '108.17', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 17, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:D_6', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '720.763', 'subgroup_hash': 763, 'subgroup_order': 720, 'subgroup_tex': 'S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056471
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.108.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.769', 'subgroup_hash': 769, 'subgroup_order': 720, 'subgroup_tex': 'C_6\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246056482
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.108.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.770', 'subgroup_hash': 770, 'subgroup_order': 720, 'subgroup_tex': 'C_6:S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246056493
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 360, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.108.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.766', 'subgroup_hash': 766, 'subgroup_order': 720, 'subgroup_tex': 'C_2\\times A_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056505
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.108.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.767', 'subgroup_hash': 767, 'subgroup_order': 720, 'subgroup_tex': 'S_3\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246056516
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.108.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.767', 'subgroup_hash': 767, 'subgroup_order': 720, 'subgroup_tex': 'S_3\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246056527
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.108.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.767', 'subgroup_hash': 767, 'subgroup_order': 720, 'subgroup_tex': 'S_3\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246056538
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.108.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.767', 'subgroup_hash': 767, 'subgroup_order': 720, 'subgroup_tex': 'S_3\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246056549
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.108.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.771', 'subgroup_hash': 771, 'subgroup_order': 720, 'subgroup_tex': 'D_6\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 246056560
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.108.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.771', 'subgroup_hash': 771, 'subgroup_order': 720, 'subgroup_tex': 'D_6\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 246056571
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.108.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.783', 'subgroup_hash': 783, 'subgroup_order': 720, 'subgroup_tex': 'F_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056582
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.108.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.769', 'subgroup_hash': 769, 'subgroup_order': 720, 'subgroup_tex': 'C_6\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246056593
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.108.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.770', 'subgroup_hash': 770, 'subgroup_order': 720, 'subgroup_tex': 'C_6:S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246056604
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 360, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.108.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.766', 'subgroup_hash': 766, 'subgroup_order': 720, 'subgroup_tex': 'C_2\\times A_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056616
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.108.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.767', 'subgroup_hash': 767, 'subgroup_order': 720, 'subgroup_tex': 'S_3\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246056627
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.108.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.767', 'subgroup_hash': 767, 'subgroup_order': 720, 'subgroup_tex': 'S_3\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246056638
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.108.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.767', 'subgroup_hash': 767, 'subgroup_order': 720, 'subgroup_tex': 'S_3\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246056649
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 360, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.108.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.763', 'subgroup_hash': 763, 'subgroup_order': 720, 'subgroup_tex': 'S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056660
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 360, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.108.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.763', 'subgroup_hash': 763, 'subgroup_order': 720, 'subgroup_tex': 'S_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056671
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.a1', 'outer_equivalence': True, 'perfect': False, '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': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056682
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.b1', 'outer_equivalence': True, 'perfect': False, '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': '648.731', 'subgroup_hash': 731, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056693
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.c1', 'outer_equivalence': True, 'perfect': False, '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': '648.733', 'subgroup_hash': 733, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056704
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.d1', 'outer_equivalence': True, 'perfect': False, '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': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246056715
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.e1', 'outer_equivalence': True, 'perfect': False, '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': '648.714', 'subgroup_hash': 714, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 246056727
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.f1', 'outer_equivalence': True, 'perfect': False, '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': '648.607', 'subgroup_hash': 607, 'subgroup_order': 648, 'subgroup_tex': 'C_2\\times C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056738
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.g1', 'outer_equivalence': True, 'perfect': False, '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': '648.555', 'subgroup_hash': 555, 'subgroup_order': 648, 'subgroup_tex': 'C_3.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056749
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.h1', 'outer_equivalence': True, 'perfect': False, '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': '648.733', 'subgroup_hash': 733, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056760
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.i1', 'outer_equivalence': True, 'perfect': False, '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': '648.555', 'subgroup_hash': 555, 'subgroup_order': 648, 'subgroup_tex': 'C_3.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.j1', 'outer_equivalence': True, 'perfect': False, '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': '648.602', 'subgroup_hash': 602, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056782
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.k1', 'outer_equivalence': True, 'perfect': False, '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': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056793
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.l1', 'outer_equivalence': True, 'perfect': False, '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': '648.555', 'subgroup_hash': 555, 'subgroup_order': 648, 'subgroup_tex': 'C_3.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056804
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.m1', 'outer_equivalence': True, 'perfect': False, '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': '648.582', 'subgroup_hash': 582, 'subgroup_order': 648, 'subgroup_tex': 'A_4\\times C_3^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056815
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.n1', 'outer_equivalence': True, 'perfect': False, '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': '648.734', 'subgroup_hash': 734, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056826
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.o1', 'outer_equivalence': True, 'perfect': False, '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': '648.715', 'subgroup_hash': 715, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 246056838
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.p1', 'outer_equivalence': True, 'perfect': False, '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': '648.716', 'subgroup_hash': 716, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 246056849
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 18, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.q1', 'outer_equivalence': True, 'perfect': False, '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': '648.731', 'subgroup_hash': 731, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056860
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.r1', 'outer_equivalence': True, 'perfect': False, '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': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056871
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 108, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.s1', 'outer_equivalence': True, 'perfect': False, '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': '648.603', 'subgroup_hash': 603, 'subgroup_order': 648, 'subgroup_tex': 'C_6\\times C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 108, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.t1', 'outer_equivalence': True, 'perfect': False, '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': '648.555', 'subgroup_hash': 555, 'subgroup_order': 648, 'subgroup_tex': 'C_3.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056893
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 108, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.u1', 'outer_equivalence': True, 'perfect': False, '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': '648.555', 'subgroup_hash': 555, 'subgroup_order': 648, 'subgroup_tex': 'C_3.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056894
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.v1', 'outer_equivalence': True, 'perfect': False, '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': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056895
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.w1', 'outer_equivalence': True, 'perfect': False, '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': '648.731', 'subgroup_hash': 731, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056896
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.x1', 'outer_equivalence': True, 'perfect': False, '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': '648.731', 'subgroup_hash': 731, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056897
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.y1', 'outer_equivalence': True, 'perfect': False, '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': '648.733', 'subgroup_hash': 733, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056899
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.z1', 'outer_equivalence': True, 'perfect': False, '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': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246056900
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.ba1', 'outer_equivalence': True, 'perfect': False, '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': '648.714', 'subgroup_hash': 714, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 246056901
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bb1', 'outer_equivalence': True, 'perfect': False, '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': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246056902
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bc1', 'outer_equivalence': True, 'perfect': False, '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': '648.610', 'subgroup_hash': 610, 'subgroup_order': 648, 'subgroup_tex': 'C_2\\times C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056903
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bd1', 'outer_equivalence': True, 'perfect': False, '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': '648.555', 'subgroup_hash': 555, 'subgroup_order': 648, 'subgroup_tex': 'C_3.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056904
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.be1', 'outer_equivalence': True, 'perfect': False, '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': '648.608', 'subgroup_hash': 608, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056905
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bf1', 'outer_equivalence': True, 'perfect': False, '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': '648.555', 'subgroup_hash': 555, 'subgroup_order': 648, 'subgroup_tex': 'C_3.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056906
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bg1', 'outer_equivalence': True, 'perfect': False, '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': '648.592', 'subgroup_hash': 592, 'subgroup_order': 648, 'subgroup_tex': 'A_4\\times C_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 246056907
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bh1', 'outer_equivalence': True, 'perfect': False, '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': '648.616', 'subgroup_hash': 616, 'subgroup_order': 648, 'subgroup_tex': 'C_2\\times A_4\\times \\He_3', 'supersolvable': False, 'sylow': 0}
  • id: 246056908
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bi1', 'outer_equivalence': True, 'perfect': False, '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': '648.557', 'subgroup_hash': 557, 'subgroup_order': 648, 'subgroup_tex': 'S_4\\times \\He_3', 'supersolvable': False, 'sylow': 0}
  • id: 246056911
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bj1', 'outer_equivalence': True, 'perfect': False, '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': '648.719', 'subgroup_hash': 719, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056912
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bk1', 'outer_equivalence': True, 'perfect': False, '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': '648.721', 'subgroup_hash': 721, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056913
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bl1', 'outer_equivalence': True, 'perfect': False, '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': '648.719', 'subgroup_hash': 719, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056914
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bm1', 'outer_equivalence': True, 'perfect': False, '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': '648.719', 'subgroup_hash': 719, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056915
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bn1', 'outer_equivalence': True, 'perfect': False, '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': '648.718', 'subgroup_hash': 718, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056916
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bo1', 'outer_equivalence': True, 'perfect': False, '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': '648.718', 'subgroup_hash': 718, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056917
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bp1', 'outer_equivalence': True, 'perfect': False, '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': '648.582', 'subgroup_hash': 582, 'subgroup_order': 648, 'subgroup_tex': 'A_4\\times C_3^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056918
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bq1', 'outer_equivalence': True, 'perfect': False, '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': '648.567', 'subgroup_hash': 567, 'subgroup_order': 648, 'subgroup_tex': '\\He_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056919
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.br1', 'outer_equivalence': True, 'perfect': False, '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': '648.592', 'subgroup_hash': 592, 'subgroup_order': 648, 'subgroup_tex': 'A_4\\times C_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 246056920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bs1', 'outer_equivalence': True, 'perfect': False, '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': '648.575', 'subgroup_hash': 575, 'subgroup_order': 648, 'subgroup_tex': '\\He_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056922
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bt1', 'outer_equivalence': True, 'perfect': False, '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': '648.567', 'subgroup_hash': 567, 'subgroup_order': 648, 'subgroup_tex': '\\He_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056923
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bu1', 'outer_equivalence': True, 'perfect': False, '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': '648.575', 'subgroup_hash': 575, 'subgroup_order': 648, 'subgroup_tex': '\\He_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056924
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bv1', 'outer_equivalence': True, 'perfect': False, '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': '648.722', 'subgroup_hash': 722, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056925
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bw1', 'outer_equivalence': True, 'perfect': False, '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': '648.720', 'subgroup_hash': 720, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246056926
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bx1', 'outer_equivalence': True, 'perfect': False, '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': '648.723', 'subgroup_hash': 723, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246056927
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.by1', 'outer_equivalence': True, 'perfect': False, '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': '648.723', 'subgroup_hash': 723, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246056928
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bz1', 'outer_equivalence': True, 'perfect': False, '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': '648.724', 'subgroup_hash': 724, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246056929
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.ca1', 'outer_equivalence': True, 'perfect': False, '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': '648.720', 'subgroup_hash': 720, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246056930
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.cb1', 'outer_equivalence': True, 'perfect': False, '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': '648.720', 'subgroup_hash': 720, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246056931
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.120.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.cc1', 'outer_equivalence': True, 'perfect': False, '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': '648.557', 'subgroup_hash': 557, 'subgroup_order': 648, 'subgroup_tex': 'S_4\\times \\He_3', 'supersolvable': False, 'sylow': 0}
  • id: 246056933
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.135.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '135.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 135, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8659', 'subgroup_hash': 8659, 'subgroup_order': 576, 'subgroup_tex': 'C_2^2:D_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 246056934
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.135.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '135.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 135, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8659', 'subgroup_hash': 8659, 'subgroup_order': 576, 'subgroup_tex': 'C_2^2:D_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 246056935
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.135.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '135.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 135, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8553', 'subgroup_hash': 8553, 'subgroup_order': 576, 'subgroup_tex': 'C_4:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056936
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.144.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.a1', 'outer_equivalence': True, 'perfect': False, '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': '540.46', 'subgroup_hash': 46, 'subgroup_order': 540, 'subgroup_tex': '\\He_3:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 246056937
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.144.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.b1', 'outer_equivalence': True, 'perfect': False, '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': '540.54', 'subgroup_hash': 54, 'subgroup_order': 540, 'subgroup_tex': 'C_3^2:D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 246056938
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 108, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.144.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.c1', 'outer_equivalence': True, 'perfect': False, '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': '540.51', 'subgroup_hash': 51, 'subgroup_order': 540, 'subgroup_tex': 'C_{15}.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056939
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 54, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.144.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.d1', 'outer_equivalence': True, 'perfect': False, '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': '540.49', 'subgroup_hash': 49, 'subgroup_order': 540, 'subgroup_tex': '\\He_3:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 246056940
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.144.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.e1', 'outer_equivalence': True, 'perfect': False, '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': '540.56', 'subgroup_hash': 56, 'subgroup_order': 540, 'subgroup_tex': '\\He_3:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 246056941
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.144.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.f1', 'outer_equivalence': True, 'perfect': False, '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': '540.33', 'subgroup_hash': 33, 'subgroup_order': 540, 'subgroup_tex': 'F_5\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056942
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.144.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.g1', 'outer_equivalence': True, 'perfect': False, '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': '540.37', 'subgroup_hash': 37, 'subgroup_order': 540, 'subgroup_tex': '\\He_3:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246056944
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.144.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.h1', 'outer_equivalence': True, 'perfect': False, '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': '540.40', 'subgroup_hash': 40, 'subgroup_order': 540, 'subgroup_tex': '\\He_3:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246056945
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.144.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.i1', 'outer_equivalence': True, 'perfect': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '540.88', 'subgroup_hash': 88, 'subgroup_order': 540, 'subgroup_tex': 'C_3\\times \\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 246056946
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.144.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.j1', 'outer_equivalence': True, 'perfect': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '540.88', 'subgroup_hash': 88, 'subgroup_order': 540, 'subgroup_tex': 'C_3\\times \\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 246056947
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 54, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.160.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.222', 'subgroup_hash': 222, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056948
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 54, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.160.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.160.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.223', 'subgroup_hash': 223, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056950
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.160.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.231', 'subgroup_hash': 231, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056951
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.160.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.229', 'subgroup_hash': 229, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056952
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.160.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.243', 'subgroup_hash': 243, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056953
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.160.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.242', 'subgroup_hash': 242, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056955
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.160.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.248', 'subgroup_hash': 248, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056956
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.162.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, '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': '480.1186', 'subgroup_hash': 1186, 'subgroup_order': 480, 'subgroup_tex': 'C_2^2\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246056957
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.a1', 'outer_equivalence': True, 'perfect': False, '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': '432.755', 'subgroup_hash': 755, 'subgroup_order': 432, 'subgroup_tex': 'S_3^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056958
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.b1', 'outer_equivalence': True, 'perfect': False, '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': '432.754', 'subgroup_hash': 754, 'subgroup_order': 432, 'subgroup_tex': 'C_6\\times \\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 246056959
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.c1', 'outer_equivalence': True, 'perfect': False, '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': '432.756', 'subgroup_hash': 756, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246056960
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.d1', 'outer_equivalence': True, 'perfect': False, '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': '432.763', 'subgroup_hash': 763, 'subgroup_order': 432, 'subgroup_tex': 'C_6\\times S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056961
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.e1', 'outer_equivalence': True, 'perfect': False, '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': '432.745', 'subgroup_hash': 745, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056962
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.f1', 'outer_equivalence': True, 'perfect': False, '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': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 246056963
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.g1', 'outer_equivalence': True, 'perfect': False, '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': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 246056964
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.h1', 'outer_equivalence': True, 'perfect': False, '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': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 246056966
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.i1', 'outer_equivalence': True, 'perfect': False, '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': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 246056967
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.j1', 'outer_equivalence': True, 'perfect': False, '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': '432.749', 'subgroup_hash': 749, 'subgroup_order': 432, 'subgroup_tex': 'A_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246056968
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.k1', 'outer_equivalence': True, 'perfect': False, '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': '432.747', 'subgroup_hash': 747, 'subgroup_order': 432, 'subgroup_tex': 'A_4:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246056969
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.l1', 'outer_equivalence': True, 'perfect': False, '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': '432.747', 'subgroup_hash': 747, 'subgroup_order': 432, 'subgroup_tex': 'A_4:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246056970
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.m1', 'outer_equivalence': True, 'perfect': False, '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': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 246056971
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.n1', 'outer_equivalence': True, 'perfect': False, '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': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 246056972
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.o1', 'outer_equivalence': True, 'perfect': False, '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': '432.745', 'subgroup_hash': 745, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056973
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.p1', 'outer_equivalence': True, 'perfect': False, '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': '432.759', 'subgroup_hash': 759, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056974
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.q1', 'outer_equivalence': True, 'perfect': False, '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': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056975
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.r1', 'outer_equivalence': True, 'perfect': False, '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': '432.759', 'subgroup_hash': 759, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056977
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.s1', 'outer_equivalence': True, 'perfect': False, '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': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056978
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.t1', 'outer_equivalence': True, 'perfect': False, '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': '432.349', 'subgroup_hash': 349, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056979
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.u1', 'outer_equivalence': True, 'perfect': False, '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': '432.317', 'subgroup_hash': 317, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056980
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.v1', 'outer_equivalence': True, 'perfect': False, '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': '432.323', 'subgroup_hash': 323, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056981
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.w1', 'outer_equivalence': True, 'perfect': False, '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': '432.323', 'subgroup_hash': 323, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056982
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.x1', 'outer_equivalence': True, 'perfect': False, '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': '432.545', 'subgroup_hash': 545, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056983
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.x2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.x2', 'outer_equivalence': True, 'perfect': False, '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': '432.545', 'subgroup_hash': 545, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056984
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.y1', 'outer_equivalence': True, 'perfect': False, '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': '432.360', 'subgroup_hash': 360, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056985
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.z1', 'outer_equivalence': True, 'perfect': False, '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': '432.360', 'subgroup_hash': 360, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056986
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.ba1', 'outer_equivalence': True, 'perfect': False, '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': '432.764', 'subgroup_hash': 764, 'subgroup_order': 432, 'subgroup_tex': 'C_6:S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056988
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bb1', 'outer_equivalence': True, 'perfect': False, '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': '432.542', 'subgroup_hash': 542, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056989
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bc1', 'outer_equivalence': True, 'perfect': False, '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': '432.558', 'subgroup_hash': 558, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056990
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bd1', 'outer_equivalence': True, 'perfect': False, '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': '432.746', 'subgroup_hash': 746, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246056991
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.be1', 'outer_equivalence': True, 'perfect': False, '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': '432.300', 'subgroup_hash': 300, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056992
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bf1', 'outer_equivalence': True, 'perfect': False, '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': '432.300', 'subgroup_hash': 300, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056993
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bg1', 'outer_equivalence': True, 'perfect': False, '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': '432.301', 'subgroup_hash': 301, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056994
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bh1', 'outer_equivalence': True, 'perfect': False, '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': '432.301', 'subgroup_hash': 301, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056995
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bi1', 'outer_equivalence': True, 'perfect': False, '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': '432.301', 'subgroup_hash': 301, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056996
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bj1', 'outer_equivalence': True, 'perfect': False, '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': '432.749', 'subgroup_hash': 749, 'subgroup_order': 432, 'subgroup_tex': 'A_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246056997
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bk1', 'outer_equivalence': True, 'perfect': False, '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': '432.748', 'subgroup_hash': 748, 'subgroup_order': 432, 'subgroup_tex': 'A_4:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246056999
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bl1', 'outer_equivalence': True, 'perfect': False, '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': '432.523', 'subgroup_hash': 523, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057000
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bm1', 'outer_equivalence': True, 'perfect': False, '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': '432.323', 'subgroup_hash': 323, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057001
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bn1', 'outer_equivalence': True, 'perfect': False, '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': '432.545', 'subgroup_hash': 545, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057002
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bo1', 'outer_equivalence': True, 'perfect': False, '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': '432.748', 'subgroup_hash': 748, 'subgroup_order': 432, 'subgroup_tex': 'A_4:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057003
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bp1', 'outer_equivalence': True, 'perfect': False, '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': '432.523', 'subgroup_hash': 523, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057004
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bq1', 'outer_equivalence': True, 'perfect': False, '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': '432.323', 'subgroup_hash': 323, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057005
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.br1', 'outer_equivalence': True, 'perfect': False, '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': '432.360', 'subgroup_hash': 360, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057006
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bs1', 'outer_equivalence': True, 'perfect': False, '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': '432.746', 'subgroup_hash': 746, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057007
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bt1', 'outer_equivalence': True, 'perfect': False, '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': '432.759', 'subgroup_hash': 759, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057008
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bu1', 'outer_equivalence': True, 'perfect': False, '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': '432.749', 'subgroup_hash': 749, 'subgroup_order': 432, 'subgroup_tex': 'A_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057010
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 108, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bv1', 'outer_equivalence': True, 'perfect': False, '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': '432.545', 'subgroup_hash': 545, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057011
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 108, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.bv2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bv2', 'outer_equivalence': True, 'perfect': False, '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': '432.545', 'subgroup_hash': 545, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057012
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 108, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bw1', 'outer_equivalence': True, 'perfect': False, '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': '432.300', 'subgroup_hash': 300, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057013
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 108, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bx1', 'outer_equivalence': True, 'perfect': False, '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': '432.300', 'subgroup_hash': 300, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057014
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 108, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.by1', 'outer_equivalence': True, 'perfect': False, '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': '432.545', 'subgroup_hash': 545, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057015
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bz1', 'outer_equivalence': True, 'perfect': False, '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': '432.755', 'subgroup_hash': 755, 'subgroup_order': 432, 'subgroup_tex': 'S_3^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057016
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.ca1', 'outer_equivalence': True, 'perfect': False, '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': '432.754', 'subgroup_hash': 754, 'subgroup_order': 432, 'subgroup_tex': 'C_6\\times \\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 246057017
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.cb1', 'outer_equivalence': True, 'perfect': False, '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': '432.756', 'subgroup_hash': 756, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246057018
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.cc1', 'outer_equivalence': True, 'perfect': False, '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': '432.763', 'subgroup_hash': 763, 'subgroup_order': 432, 'subgroup_tex': 'C_6\\times S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057019
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.cd1', 'outer_equivalence': True, 'perfect': False, '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': '432.763', 'subgroup_hash': 763, 'subgroup_order': 432, 'subgroup_tex': 'C_6\\times S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057022
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.ce1', 'outer_equivalence': True, 'perfect': False, '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': '432.745', 'subgroup_hash': 745, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057023
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.cf1', 'outer_equivalence': True, 'perfect': False, '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': '432.745', 'subgroup_hash': 745, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057024
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.cg1', 'outer_equivalence': True, 'perfect': False, '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': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 246057025
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.ch1', 'outer_equivalence': True, 'perfect': False, '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': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 246057026
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.ci1', 'outer_equivalence': True, 'perfect': False, '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': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 246057027
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.cj1', 'outer_equivalence': True, 'perfect': False, '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': '432.749', 'subgroup_hash': 749, 'subgroup_order': 432, 'subgroup_tex': 'A_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057028
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.ck1', 'outer_equivalence': True, 'perfect': False, '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': '432.747', 'subgroup_hash': 747, 'subgroup_order': 432, 'subgroup_tex': 'A_4:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057029
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.cl1', 'outer_equivalence': True, 'perfect': False, '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': '432.747', 'subgroup_hash': 747, 'subgroup_order': 432, 'subgroup_tex': 'A_4:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057030
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.cm1', 'outer_equivalence': True, 'perfect': False, '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': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 246057031
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.cn1', 'outer_equivalence': True, 'perfect': False, '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': '432.745', 'subgroup_hash': 745, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057033
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.co1', 'outer_equivalence': True, 'perfect': False, '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': '432.745', 'subgroup_hash': 745, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057034
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.cp1', 'outer_equivalence': True, 'perfect': False, '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': '432.545', 'subgroup_hash': 545, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057035
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.cp2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.cp2', 'outer_equivalence': True, 'perfect': False, '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': '432.545', 'subgroup_hash': 545, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057036
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.cq1', 'outer_equivalence': True, 'perfect': False, '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': '432.324', 'subgroup_hash': 324, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057037
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.cr1', 'outer_equivalence': True, 'perfect': False, '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': '432.324', 'subgroup_hash': 324, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057038
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 54, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.cs1', 'outer_equivalence': True, 'perfect': False, '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': '432.385', 'subgroup_hash': 385, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057039
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.ct1', 'outer_equivalence': True, 'perfect': False, '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': '432.321', 'subgroup_hash': 321, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057040
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 54, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.cu1', 'outer_equivalence': True, 'perfect': False, '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': '432.390', 'subgroup_hash': 390, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057041
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 54, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.cv1', 'outer_equivalence': True, 'perfect': False, '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': '432.390', 'subgroup_hash': 390, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057042
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 54, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.cw1', 'outer_equivalence': True, 'perfect': False, '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': '432.561', 'subgroup_hash': 561, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057044
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.cx1', 'outer_equivalence': True, 'perfect': False, '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': '432.302', 'subgroup_hash': 302, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057045
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.cy1', 'outer_equivalence': True, 'perfect': False, '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': '432.300', 'subgroup_hash': 300, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057046
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.cz1', 'outer_equivalence': True, 'perfect': False, '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': '432.300', 'subgroup_hash': 300, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057047
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.da1', 'outer_equivalence': True, 'perfect': False, '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': '432.302', 'subgroup_hash': 302, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057048
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.db1', 'outer_equivalence': True, 'perfect': False, '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': '432.302', 'subgroup_hash': 302, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057049
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.dc1', 'outer_equivalence': True, 'perfect': False, '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': '432.324', 'subgroup_hash': 324, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057050
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.dd1', 'outer_equivalence': True, 'perfect': False, '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': '432.545', 'subgroup_hash': 545, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057051
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.de1', 'outer_equivalence': True, 'perfect': False, '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': '432.324', 'subgroup_hash': 324, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057052
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 54, 'counter': 428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.df1', 'outer_equivalence': True, 'perfect': False, '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': '432.390', 'subgroup_hash': 390, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.dg1', 'outer_equivalence': True, 'perfect': False, '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': '432.322', 'subgroup_hash': 322, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057055
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.dg2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.dg2', 'outer_equivalence': True, 'perfect': False, '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': '432.324', 'subgroup_hash': 324, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057056
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.dh1', 'outer_equivalence': True, 'perfect': False, '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': '432.323', 'subgroup_hash': 323, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057057
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.di1', 'outer_equivalence': True, 'perfect': False, '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': '432.323', 'subgroup_hash': 323, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057058
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.dj1', 'outer_equivalence': True, 'perfect': False, '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': '432.350', 'subgroup_hash': 350, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057059
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.dk1', 'outer_equivalence': True, 'perfect': False, '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': '432.320', 'subgroup_hash': 320, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057060
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.dl1', 'outer_equivalence': True, 'perfect': False, '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': '432.386', 'subgroup_hash': 386, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057061
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.dm1', 'outer_equivalence': True, 'perfect': False, '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': '432.360', 'subgroup_hash': 360, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057062
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.dn1', 'outer_equivalence': True, 'perfect': False, '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': '432.390', 'subgroup_hash': 390, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057063
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.do1', 'outer_equivalence': True, 'perfect': False, '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': '432.360', 'subgroup_hash': 360, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057064
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.dp1', 'outer_equivalence': True, 'perfect': False, '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': '432.390', 'subgroup_hash': 390, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057066
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.dq1', 'outer_equivalence': True, 'perfect': False, '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': '432.761', 'subgroup_hash': 761, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057067
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.dr1', 'outer_equivalence': True, 'perfect': False, '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': '432.535', 'subgroup_hash': 535, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057068
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.ds1', 'outer_equivalence': True, 'perfect': False, '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': '432.377', 'subgroup_hash': 377, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057069
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.dt1', 'outer_equivalence': True, 'perfect': False, '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': '432.762', 'subgroup_hash': 762, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057070
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.du1', 'outer_equivalence': True, 'perfect': False, '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': '432.761', 'subgroup_hash': 761, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057071
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.dv1', 'outer_equivalence': True, 'perfect': False, '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': '432.538', 'subgroup_hash': 538, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057072
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.dw1', 'outer_equivalence': True, 'perfect': False, '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': '432.399', 'subgroup_hash': 399, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057073
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.dx1', 'outer_equivalence': True, 'perfect': False, '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': '432.761', 'subgroup_hash': 761, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057074
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.dy1', 'outer_equivalence': True, 'perfect': False, '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': '432.538', 'subgroup_hash': 538, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057075
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.dz1', 'outer_equivalence': True, 'perfect': False, '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': '432.745', 'subgroup_hash': 745, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057077
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.ea1', 'outer_equivalence': True, 'perfect': False, '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': '432.746', 'subgroup_hash': 746, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057078
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.eb1', 'outer_equivalence': True, 'perfect': False, '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': '432.745', 'subgroup_hash': 745, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057079
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.ec1', 'outer_equivalence': True, 'perfect': False, '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': '432.745', 'subgroup_hash': 745, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057080
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.ed1', 'outer_equivalence': True, 'perfect': False, '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': '432.404', 'subgroup_hash': 404, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}.C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057081
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.ee1', 'outer_equivalence': True, 'perfect': False, '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': '432.760', 'subgroup_hash': 760, 'subgroup_order': 432, 'subgroup_tex': 'A_4:C_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057082
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.ef1', 'outer_equivalence': True, 'perfect': False, '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': '432.760', 'subgroup_hash': 760, 'subgroup_order': 432, 'subgroup_tex': 'A_4:C_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057083
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.eg1', 'outer_equivalence': True, 'perfect': False, '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': '432.301', 'subgroup_hash': 301, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057084
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.eh1', 'outer_equivalence': True, 'perfect': False, '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': '432.301', 'subgroup_hash': 301, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057085
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.ei1', 'outer_equivalence': True, 'perfect': False, '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': '432.302', 'subgroup_hash': 302, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057086
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.ej1', 'outer_equivalence': True, 'perfect': False, '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': '432.302', 'subgroup_hash': 302, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057088
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.ek1', 'outer_equivalence': True, 'perfect': False, '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': '432.301', 'subgroup_hash': 301, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057089
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.el1', 'outer_equivalence': True, 'perfect': False, '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': '432.747', 'subgroup_hash': 747, 'subgroup_order': 432, 'subgroup_tex': 'A_4:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057090
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.em1', 'outer_equivalence': True, 'perfect': False, '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': '432.747', 'subgroup_hash': 747, 'subgroup_order': 432, 'subgroup_tex': 'A_4:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057091
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.en1', 'outer_equivalence': True, 'perfect': False, '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': '432.324', 'subgroup_hash': 324, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057092
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.eo1', 'outer_equivalence': True, 'perfect': False, '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': '432.748', 'subgroup_hash': 748, 'subgroup_order': 432, 'subgroup_tex': 'A_4:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057093
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.ep1', 'outer_equivalence': True, 'perfect': False, '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': '432.523', 'subgroup_hash': 523, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057094
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.eq1', 'outer_equivalence': True, 'perfect': False, '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': '432.323', 'subgroup_hash': 323, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057095
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.er1', 'outer_equivalence': True, 'perfect': False, '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': '432.747', 'subgroup_hash': 747, 'subgroup_order': 432, 'subgroup_tex': 'A_4:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057096
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.es1', 'outer_equivalence': True, 'perfect': False, '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': '432.748', 'subgroup_hash': 748, 'subgroup_order': 432, 'subgroup_tex': 'A_4:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057097
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.et1', 'outer_equivalence': True, 'perfect': False, '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': '432.523', 'subgroup_hash': 523, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057099
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.eu1', 'outer_equivalence': True, 'perfect': False, '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': '432.323', 'subgroup_hash': 323, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057100
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.ev1', 'outer_equivalence': True, 'perfect': False, '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': '432.747', 'subgroup_hash': 747, 'subgroup_order': 432, 'subgroup_tex': 'A_4:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057101
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.ew1', 'outer_equivalence': True, 'perfect': False, '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': '432.360', 'subgroup_hash': 360, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057102
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.ex1', 'outer_equivalence': True, 'perfect': False, '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': '432.390', 'subgroup_hash': 390, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057103
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.ey1', 'outer_equivalence': True, 'perfect': False, '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': '432.745', 'subgroup_hash': 745, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057104
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.ez1', 'outer_equivalence': True, 'perfect': False, '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': '432.746', 'subgroup_hash': 746, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057105
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.fa1', 'outer_equivalence': True, 'perfect': False, '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': '432.745', 'subgroup_hash': 745, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057106
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.180.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.fb1', 'outer_equivalence': True, 'perfect': False, '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': '432.745', 'subgroup_hash': 745, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057107
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 360, 'counter': 478, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '77760.bo.216.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': False, 'normal': True, 'old_label': '216.a1', 'outer_equivalence': True, 'perfect': True, 'proper': True, 'quotient': '216.102', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 102, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6.S_3^2', 'simple': True, 'solvable': False, 'special_labels': ['PC', 'D3', 'PC', 'D3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '360.118', 'subgroup_hash': 118, 'subgroup_order': 360, 'subgroup_tex': 'A_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057108
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.216.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.122', 'subgroup_hash': 122, 'subgroup_order': 360, 'subgroup_tex': 'C_6\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057110
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.216.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.126', 'subgroup_hash': 126, 'subgroup_order': 360, 'subgroup_tex': 'D_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057111
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.216.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.128', 'subgroup_hash': 128, 'subgroup_order': 360, 'subgroup_tex': 'D_5.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057112
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.216.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.121', 'subgroup_hash': 121, 'subgroup_order': 360, 'subgroup_tex': 'S_3\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057113
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.216.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.121', 'subgroup_hash': 121, 'subgroup_order': 360, 'subgroup_tex': 'S_3\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057114
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.216.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.127', 'subgroup_hash': 127, 'subgroup_order': 360, 'subgroup_tex': 'C_3:S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246057115
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.216.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.129', 'subgroup_hash': 129, 'subgroup_order': 360, 'subgroup_tex': 'D_5.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057116
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.216.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.137', 'subgroup_hash': 137, 'subgroup_order': 360, 'subgroup_tex': 'D_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057117
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.216.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.122', 'subgroup_hash': 122, 'subgroup_order': 360, 'subgroup_tex': 'C_6\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057118
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.216.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.126', 'subgroup_hash': 126, 'subgroup_order': 360, 'subgroup_tex': 'D_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057119
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.216.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.128', 'subgroup_hash': 128, 'subgroup_order': 360, 'subgroup_tex': 'D_5.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057121
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.216.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.126', 'subgroup_hash': 126, 'subgroup_order': 360, 'subgroup_tex': 'D_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057122
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.216.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.121', 'subgroup_hash': 121, 'subgroup_order': 360, 'subgroup_tex': 'S_3\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057123
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.216.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.121', 'subgroup_hash': 121, 'subgroup_order': 360, 'subgroup_tex': 'S_3\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057124
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.216.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.119', 'subgroup_hash': 119, 'subgroup_order': 360, 'subgroup_tex': 'C_3\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057125
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.216.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.119', 'subgroup_hash': 119, 'subgroup_order': 360, 'subgroup_tex': 'C_3\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057126
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.216.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.119', 'subgroup_hash': 119, 'subgroup_order': 360, 'subgroup_tex': 'C_3\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057127
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.216.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.119', 'subgroup_hash': 119, 'subgroup_order': 360, 'subgroup_tex': 'C_3\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057128
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.216.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.120', 'subgroup_hash': 120, 'subgroup_order': 360, 'subgroup_tex': 'C_3:S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057129
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.216.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.120', 'subgroup_hash': 120, 'subgroup_order': 360, 'subgroup_tex': 'C_3:S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057130
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.216.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.119', 'subgroup_hash': 119, 'subgroup_order': 360, 'subgroup_tex': 'C_3\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057133
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.216.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.120', 'subgroup_hash': 120, 'subgroup_order': 360, 'subgroup_tex': 'C_3:S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057134
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.216.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.120', 'subgroup_hash': 120, 'subgroup_order': 360, 'subgroup_tex': 'C_3:S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057135
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.a1', 'outer_equivalence': True, 'perfect': False, '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': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057136
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.b1', 'outer_equivalence': True, 'perfect': False, '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': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057137
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.c1', 'outer_equivalence': True, 'perfect': False, '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': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057138
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.d1', 'outer_equivalence': True, 'perfect': False, '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': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057139
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.e1', 'outer_equivalence': True, 'perfect': False, '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': '324.138', 'subgroup_hash': 138, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057140
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 18, 'counter': 507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.f1', 'outer_equivalence': True, 'perfect': False, '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': '324.116', 'subgroup_hash': 116, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057141
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 18, 'counter': 508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.g1', 'outer_equivalence': True, 'perfect': False, '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': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057142
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.h1', 'outer_equivalence': True, 'perfect': False, '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': '324.116', 'subgroup_hash': 116, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057144
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.i1', 'outer_equivalence': True, 'perfect': False, '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': '324.116', 'subgroup_hash': 116, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057145
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.j1', 'outer_equivalence': True, 'perfect': False, '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': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057146
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 18, 'counter': 512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.k1', 'outer_equivalence': True, 'perfect': False, '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': '324.117', 'subgroup_hash': 117, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057147
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 18, 'counter': 513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.l1', 'outer_equivalence': True, 'perfect': False, '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': '324.167', 'subgroup_hash': 167, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057148
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.m1', 'outer_equivalence': True, 'perfect': False, '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': '324.117', 'subgroup_hash': 117, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.n1', 'outer_equivalence': True, 'perfect': False, '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': '324.121', 'subgroup_hash': 121, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057150
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.o1', 'outer_equivalence': True, 'perfect': False, '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': '324.121', 'subgroup_hash': 121, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057151
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.p1', 'outer_equivalence': True, 'perfect': False, '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': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057152
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.q1', 'outer_equivalence': True, 'perfect': False, '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': '324.121', 'subgroup_hash': 121, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057153
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 18, 'counter': 519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.r1', 'outer_equivalence': True, 'perfect': False, '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': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057155
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 108, 'counter': 520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.s1', 'outer_equivalence': True, 'perfect': False, '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': '324.117', 'subgroup_hash': 117, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057156
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.t1', 'outer_equivalence': True, 'perfect': False, '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': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057157
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.u1', 'outer_equivalence': True, 'perfect': False, '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': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057158
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.v1', 'outer_equivalence': True, 'perfect': False, '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': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057159
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.w1', 'outer_equivalence': True, 'perfect': False, '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': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057160
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.x1', 'outer_equivalence': True, 'perfect': False, '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': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057161
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.y1', 'outer_equivalence': True, 'perfect': False, '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': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057162
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.z1', 'outer_equivalence': True, 'perfect': False, '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': '324.145', 'subgroup_hash': 145, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057163
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.ba1', 'outer_equivalence': True, 'perfect': False, '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': '324.122', 'subgroup_hash': 122, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057164
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bb1', 'outer_equivalence': True, 'perfect': False, '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': '324.122', 'subgroup_hash': 122, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057166
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bc1', 'outer_equivalence': True, 'perfect': False, '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': '324.117', 'subgroup_hash': 117, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057167
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bd1', 'outer_equivalence': True, 'perfect': False, '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': '324.124', 'subgroup_hash': 124, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057168
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.be1', 'outer_equivalence': True, 'perfect': False, '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': '324.124', 'subgroup_hash': 124, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057169
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bf1', 'outer_equivalence': True, 'perfect': False, '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': '324.144', 'subgroup_hash': 144, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057170
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bg1', 'outer_equivalence': True, 'perfect': False, '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': '324.150', 'subgroup_hash': 150, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057171
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bh1', 'outer_equivalence': True, 'perfect': False, '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': '324.116', 'subgroup_hash': 116, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057172
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bi1', 'outer_equivalence': True, 'perfect': False, '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': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057173
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bj1', 'outer_equivalence': True, 'perfect': False, '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': '324.116', 'subgroup_hash': 116, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057174
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bk1', 'outer_equivalence': True, 'perfect': False, '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': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057175
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bl1', 'outer_equivalence': True, 'perfect': False, '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': '324.122', 'subgroup_hash': 122, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057177
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bm1', 'outer_equivalence': True, 'perfect': False, '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': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057178
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bn1', 'outer_equivalence': True, 'perfect': False, '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': '324.122', 'subgroup_hash': 122, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057179
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bo1', 'outer_equivalence': True, 'perfect': False, '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': '324.122', 'subgroup_hash': 122, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057180
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bp1', 'outer_equivalence': True, 'perfect': False, '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': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057181
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bq1', 'outer_equivalence': True, 'perfect': False, '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': '324.139', 'subgroup_hash': 139, 'subgroup_order': 324, 'subgroup_tex': 'D_6\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057182
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.br1', 'outer_equivalence': True, 'perfect': False, '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': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057183
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bs1', 'outer_equivalence': True, 'perfect': False, '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': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057184
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bt1', 'outer_equivalence': True, 'perfect': False, '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': '324.116', 'subgroup_hash': 116, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057185
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bu1', 'outer_equivalence': True, 'perfect': False, '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': '324.122', 'subgroup_hash': 122, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057186
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bv1', 'outer_equivalence': True, 'perfect': False, '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': '324.130', 'subgroup_hash': 130, 'subgroup_order': 324, 'subgroup_tex': 'A_4\\times \\He_3', 'supersolvable': False, 'sylow': 0}
  • id: 246057188
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bw1', 'outer_equivalence': True, 'perfect': False, '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': '324.167', 'subgroup_hash': 167, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057189
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bx1', 'outer_equivalence': True, 'perfect': False, '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': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057190
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.by1', 'outer_equivalence': True, 'perfect': False, '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': '324.167', 'subgroup_hash': 167, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057191
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bz1', 'outer_equivalence': True, 'perfect': False, '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': '324.167', 'subgroup_hash': 167, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057192
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.ca1', 'outer_equivalence': True, 'perfect': False, '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': '324.161', 'subgroup_hash': 161, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246057193
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.cb1', 'outer_equivalence': True, 'perfect': False, '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': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057194
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.cc1', 'outer_equivalence': True, 'perfect': False, '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': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057195
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.cd1', 'outer_equivalence': True, 'perfect': False, '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': '324.163', 'subgroup_hash': 163, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057196
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.ce1', 'outer_equivalence': True, 'perfect': False, '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': '324.161', 'subgroup_hash': 161, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246057197
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.cf1', 'outer_equivalence': True, 'perfect': False, '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': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057199
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.cg1', 'outer_equivalence': True, 'perfect': False, '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': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057200
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.ch1', 'outer_equivalence': True, 'perfect': False, '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': '324.121', 'subgroup_hash': 121, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057201
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.ci1', 'outer_equivalence': True, 'perfect': False, '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': '324.124', 'subgroup_hash': 124, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057202
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.cj1', 'outer_equivalence': True, 'perfect': False, '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': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057203
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.ck1', 'outer_equivalence': True, 'perfect': False, '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': '324.124', 'subgroup_hash': 124, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057204
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.cl1', 'outer_equivalence': True, 'perfect': False, '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': '324.121', 'subgroup_hash': 121, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057205
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.cm1', 'outer_equivalence': True, 'perfect': False, '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': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057206
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.240.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.cn1', 'outer_equivalence': True, 'perfect': False, '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': '324.121', 'subgroup_hash': 121, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057207
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1034', 'subgroup_hash': 1034, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057208
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057210
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1033', 'subgroup_hash': 1033, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057211
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057212
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1031', 'subgroup_hash': 1031, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057213
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.951', 'subgroup_hash': 951, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057214
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057215
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057216
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057217
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.976', 'subgroup_hash': 976, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 246057218
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057219
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057221
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057222
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057223
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.992', 'subgroup_hash': 992, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057224
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057225
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057226
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057227
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057228
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057229
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1037', 'subgroup_hash': 1037, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057230
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057232
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057233
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1037', 'subgroup_hash': 1037, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057234
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057235
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057236
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.952', 'subgroup_hash': 952, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057237
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057238
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057239
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.977', 'subgroup_hash': 977, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 246057240
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1007', 'subgroup_hash': 1007, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057241
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057244
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.950', 'subgroup_hash': 950, 'subgroup_order': 288, 'subgroup_tex': 'C_2.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057245
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057246
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057247
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1040', 'subgroup_hash': 1040, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057248
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057249
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1034', 'subgroup_hash': 1034, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057250
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057251
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1033', 'subgroup_hash': 1033, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057252
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057253
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.951', 'subgroup_hash': 951, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057255
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057257
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.976', 'subgroup_hash': 976, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 246057258
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057259
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057261
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.992', 'subgroup_hash': 992, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.992', 'subgroup_hash': 992, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057266
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057267
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.270.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057268
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 54, 'counter': 622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.288.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.a1', 'outer_equivalence': True, 'perfect': False, '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': '270.10', 'subgroup_hash': 10, 'subgroup_order': 270, 'subgroup_tex': 'C_3^2:C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 246057269
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 54, 'counter': 623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.288.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.b1', 'outer_equivalence': True, 'perfect': False, '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': '270.17', 'subgroup_hash': 17, 'subgroup_order': 270, 'subgroup_tex': '\\He_3:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 246057270
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.288.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.c1', 'outer_equivalence': True, 'perfect': False, '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': '270.6', 'subgroup_hash': 6, 'subgroup_order': 270, 'subgroup_tex': 'D_5\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057271
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.288.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.d1', 'outer_equivalence': True, 'perfect': False, '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': '270.14', 'subgroup_hash': 14, 'subgroup_order': 270, 'subgroup_tex': 'C_3^2:D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 246057272
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.288.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.e1', 'outer_equivalence': True, 'perfect': False, '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': '270.19', 'subgroup_hash': 19, 'subgroup_order': 270, 'subgroup_tex': 'C_3^2:D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 246057273
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 627, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '77760.bo.320.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '320.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 3}
  • id: 246057274
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.324.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, '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': '240.189', 'subgroup_hash': 189, 'subgroup_order': 240, 'subgroup_tex': 'C_2\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057275
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.324.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, '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': '240.189', 'subgroup_hash': 189, 'subgroup_order': 240, 'subgroup_tex': 'C_2\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057277
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.324.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.190', 'subgroup_hash': 190, 'subgroup_order': 240, 'subgroup_tex': 'C_2^2\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057278
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.324.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.195', 'subgroup_hash': 195, 'subgroup_order': 240, 'subgroup_tex': 'D_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246057279
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.324.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.195', 'subgroup_hash': 195, 'subgroup_order': 240, 'subgroup_tex': 'D_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246057280
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.324.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, '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': '240.189', 'subgroup_hash': 189, 'subgroup_order': 240, 'subgroup_tex': 'C_2\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057281
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.324.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, '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': '240.189', 'subgroup_hash': 189, 'subgroup_order': 240, 'subgroup_tex': 'C_2\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246057282
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.a1', 'outer_equivalence': True, 'perfect': False, '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': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057283
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.b1', 'outer_equivalence': True, 'perfect': False, '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': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057284
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.c1', 'outer_equivalence': True, 'perfect': False, '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': '216.172', 'subgroup_hash': 172, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057285
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.d1', 'outer_equivalence': True, 'perfect': False, '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': '216.168', 'subgroup_hash': 168, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246057286
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.e1', 'outer_equivalence': True, 'perfect': False, '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': '216.169', 'subgroup_hash': 169, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057288
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.f1', 'outer_equivalence': True, 'perfect': False, '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': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057289
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.g1', 'outer_equivalence': True, 'perfect': False, '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': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057290
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.h1', 'outer_equivalence': True, 'perfect': False, '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': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057291
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.i1', 'outer_equivalence': True, 'perfect': False, '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': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057292
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.j1', 'outer_equivalence': True, 'perfect': False, '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': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057293
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.k1', 'outer_equivalence': True, 'perfect': False, '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': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057294
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.l1', 'outer_equivalence': True, 'perfect': False, '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': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057295
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.m1', 'outer_equivalence': True, 'perfect': False, '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': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057296
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.n1', 'outer_equivalence': True, 'perfect': False, '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': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057297
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.o1', 'outer_equivalence': True, 'perfect': False, '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': '216.166', 'subgroup_hash': 166, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057299
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.p1', 'outer_equivalence': True, 'perfect': False, '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': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057300
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.q1', 'outer_equivalence': True, 'perfect': False, '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': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057301
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.r1', 'outer_equivalence': True, 'perfect': False, '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': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 246057302
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.s1', 'outer_equivalence': True, 'perfect': False, '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': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 246057303
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.t1', 'outer_equivalence': True, 'perfect': False, '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': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 246057304
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.u1', 'outer_equivalence': True, 'perfect': False, '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': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 246057305
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.v1', 'outer_equivalence': True, 'perfect': False, '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': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057306
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.w1', 'outer_equivalence': True, 'perfect': False, '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': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057307
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.x1', 'outer_equivalence': True, 'perfect': False, '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': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057308
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.y1', 'outer_equivalence': True, 'perfect': False, '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': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057310
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.z1', 'outer_equivalence': True, 'perfect': False, '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': '216.172', 'subgroup_hash': 172, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057311
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ba1', 'outer_equivalence': True, 'perfect': False, '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': '216.102', 'subgroup_hash': 102, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057312
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bb1', 'outer_equivalence': True, 'perfect': False, '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': '216.102', 'subgroup_hash': 102, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057313
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 54, 'counter': 663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.bb2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bb2', 'outer_equivalence': True, 'perfect': False, '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': '216.102', 'subgroup_hash': 102, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057314
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bc1', 'outer_equivalence': True, 'perfect': False, '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': '216.110', 'subgroup_hash': 110, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057315
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 54, 'counter': 665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.bc2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bc2', 'outer_equivalence': True, 'perfect': False, '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': '216.110', 'subgroup_hash': 110, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057316
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bd1', 'outer_equivalence': True, 'perfect': False, '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': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057317
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.be1', 'outer_equivalence': True, 'perfect': False, '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': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057318
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bf1', 'outer_equivalence': True, 'perfect': False, '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': '216.102', 'subgroup_hash': 102, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057319
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 54, 'counter': 669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.bf2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bf2', 'outer_equivalence': True, 'perfect': False, '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': '216.102', 'subgroup_hash': 102, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057321
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bg1', 'outer_equivalence': True, 'perfect': False, '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': '216.50', 'subgroup_hash': 50, 'subgroup_order': 216, 'subgroup_tex': 'C_4\\times C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057322
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bh1', 'outer_equivalence': True, 'perfect': False, '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': '216.50', 'subgroup_hash': 50, 'subgroup_order': 216, 'subgroup_tex': 'C_4\\times C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057323
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bi1', 'outer_equivalence': True, 'perfect': False, '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': '216.34', 'subgroup_hash': 34, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057324
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bj1', 'outer_equivalence': True, 'perfect': False, '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': '216.34', 'subgroup_hash': 34, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057325
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bk1', 'outer_equivalence': True, 'perfect': False, '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': '216.102', 'subgroup_hash': 102, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057326
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bl1', 'outer_equivalence': True, 'perfect': False, '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': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057327
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 676, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bm1', 'outer_equivalence': True, 'perfect': False, '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': '216.167', 'subgroup_hash': 167, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057328
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 677, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bn1', 'outer_equivalence': True, 'perfect': False, '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': '216.99', 'subgroup_hash': 99, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057329
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 678, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bo1', 'outer_equivalence': True, 'perfect': False, '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': '216.110', 'subgroup_hash': 110, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057330
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 679, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bp1', 'outer_equivalence': True, 'perfect': False, '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': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057332
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bq1', 'outer_equivalence': True, 'perfect': False, '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': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057333
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.br1', 'outer_equivalence': True, 'perfect': False, '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': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057334
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 108, 'counter': 682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bs1', 'outer_equivalence': True, 'perfect': False, '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': '216.102', 'subgroup_hash': 102, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057335
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 108, 'counter': 683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bt1', 'outer_equivalence': True, 'perfect': False, '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': '216.102', 'subgroup_hash': 102, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057336
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bu1', 'outer_equivalence': True, 'perfect': False, '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': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057337
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bv1', 'outer_equivalence': True, 'perfect': False, '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': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057338
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bw1', 'outer_equivalence': True, 'perfect': False, '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': '216.172', 'subgroup_hash': 172, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057339
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bx1', 'outer_equivalence': True, 'perfect': False, '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': '216.168', 'subgroup_hash': 168, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246057340
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.by1', 'outer_equivalence': True, 'perfect': False, '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': '216.169', 'subgroup_hash': 169, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057341
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bz1', 'outer_equivalence': True, 'perfect': False, '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': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057343
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ca1', 'outer_equivalence': True, 'perfect': False, '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': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057344
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cb1', 'outer_equivalence': True, 'perfect': False, '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': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057345
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cc1', 'outer_equivalence': True, 'perfect': False, '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': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057346
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cd1', 'outer_equivalence': True, 'perfect': False, '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': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057347
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ce1', 'outer_equivalence': True, 'perfect': False, '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': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057348
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cf1', 'outer_equivalence': True, 'perfect': False, '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': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057349
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cg1', 'outer_equivalence': True, 'perfect': False, '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': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057350
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ch1', 'outer_equivalence': True, 'perfect': False, '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': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057351
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ci1', 'outer_equivalence': True, 'perfect': False, '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': '216.166', 'subgroup_hash': 166, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057352
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cj1', 'outer_equivalence': True, 'perfect': False, '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': '216.166', 'subgroup_hash': 166, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057355
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ck1', 'outer_equivalence': True, 'perfect': False, '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': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057356
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cl1', 'outer_equivalence': True, 'perfect': False, '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': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 246057357
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cm1', 'outer_equivalence': True, 'perfect': False, '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': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 246057358
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cn1', 'outer_equivalence': True, 'perfect': False, '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': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 246057359
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.co1', 'outer_equivalence': True, 'perfect': False, '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': '216.102', 'subgroup_hash': 102, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057360
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 54, 'counter': 705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.co2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.co2', 'outer_equivalence': True, 'perfect': False, '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': '216.102', 'subgroup_hash': 102, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057361
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 54, 'counter': 706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cp1', 'outer_equivalence': True, 'perfect': False, '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': '216.113', 'subgroup_hash': 113, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057362
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 54, 'counter': 707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.cp2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cp2', 'outer_equivalence': True, 'perfect': False, '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': '216.113', 'subgroup_hash': 113, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057363
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cq1', 'outer_equivalence': True, 'perfect': False, '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': '216.102', 'subgroup_hash': 102, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057364
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 54, 'counter': 709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.cq2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cq2', 'outer_equivalence': True, 'perfect': False, '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': '216.102', 'subgroup_hash': 102, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057366
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 710, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cr1', 'outer_equivalence': True, 'perfect': False, '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': '216.102', 'subgroup_hash': 102, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057367
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 54, 'counter': 711, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cs1', 'outer_equivalence': True, 'perfect': False, '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': '216.67', 'subgroup_hash': 67, 'subgroup_order': 216, 'subgroup_tex': 'C_4\\times C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057368
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 54, 'counter': 712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ct1', 'outer_equivalence': True, 'perfect': False, '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': '216.67', 'subgroup_hash': 67, 'subgroup_order': 216, 'subgroup_tex': 'C_4\\times C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057369
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cu1', 'outer_equivalence': True, 'perfect': False, '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': '216.36', 'subgroup_hash': 36, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057370
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cv1', 'outer_equivalence': True, 'perfect': False, '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': '216.36', 'subgroup_hash': 36, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057371
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 54, 'counter': 715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cw1', 'outer_equivalence': True, 'perfect': False, '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': '216.113', 'subgroup_hash': 113, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057372
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 27, 'counter': 716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cx1', 'outer_equivalence': True, 'perfect': False, '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': '216.102', 'subgroup_hash': 102, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057373
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 27, 'counter': 717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.cx2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cx2', 'outer_equivalence': True, 'perfect': False, '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': '216.102', 'subgroup_hash': 102, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057374
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 27, 'counter': 718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.cx3', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cx3', 'outer_equivalence': True, 'perfect': False, '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': '216.102', 'subgroup_hash': 102, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057375
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 27, 'counter': 719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cy1', 'outer_equivalence': True, 'perfect': False, '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': '216.110', 'subgroup_hash': 110, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057377
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 27, 'counter': 720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.cy2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cy2', 'outer_equivalence': True, 'perfect': False, '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': '216.110', 'subgroup_hash': 110, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057378
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cz1', 'outer_equivalence': True, 'perfect': False, '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': '216.60', 'subgroup_hash': 60, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057379
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 27, 'counter': 722, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.da1', 'outer_equivalence': True, 'perfect': False, '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': '216.113', 'subgroup_hash': 113, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057380
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 27, 'counter': 723, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.da2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.da2', 'outer_equivalence': True, 'perfect': False, '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': '216.113', 'subgroup_hash': 113, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057381
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.db1', 'outer_equivalence': True, 'perfect': False, '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': '216.72', 'subgroup_hash': 72, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057382
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.dc1', 'outer_equivalence': True, 'perfect': False, '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': '216.60', 'subgroup_hash': 60, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057383
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.dd1', 'outer_equivalence': True, 'perfect': False, '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': '216.72', 'subgroup_hash': 72, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057384
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 27, 'counter': 727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.de1', 'outer_equivalence': True, 'perfect': False, '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': '216.74', 'subgroup_hash': 74, 'subgroup_order': 216, 'subgroup_tex': 'C_6.C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057385
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 27, 'counter': 728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.df1', 'outer_equivalence': True, 'perfect': False, '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': '216.71', 'subgroup_hash': 71, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2.S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057386
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 27, 'counter': 729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.dg1', 'outer_equivalence': True, 'perfect': False, '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': '216.59', 'subgroup_hash': 59, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2.C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057388
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 730, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.dh1', 'outer_equivalence': True, 'perfect': False, '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': '216.77', 'subgroup_hash': 77, 'subgroup_order': 216, 'subgroup_tex': 'D_4\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057389
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.di1', 'outer_equivalence': True, 'perfect': False, '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': '216.77', 'subgroup_hash': 77, 'subgroup_order': 216, 'subgroup_tex': 'D_4\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057390
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.dj1', 'outer_equivalence': True, 'perfect': False, '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': '216.173', 'subgroup_hash': 173, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057391
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.dk1', 'outer_equivalence': True, 'perfect': False, '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': '216.107', 'subgroup_hash': 107, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057392
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 27, 'counter': 734, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.dl1', 'outer_equivalence': True, 'perfect': False, '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': '216.115', 'subgroup_hash': 115, 'subgroup_order': 216, 'subgroup_tex': 'C_2^3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057393
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 735, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.dm1', 'outer_equivalence': True, 'perfect': False, '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': '216.173', 'subgroup_hash': 173, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057394
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 736, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.dn1', 'outer_equivalence': True, 'perfect': False, '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': '216.107', 'subgroup_hash': 107, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057395
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 737, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.do1', 'outer_equivalence': True, 'perfect': False, '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': '216.163', 'subgroup_hash': 163, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057396
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.dp1', 'outer_equivalence': True, 'perfect': False, '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': '216.163', 'subgroup_hash': 163, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057397
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 739, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.dq1', 'outer_equivalence': True, 'perfect': False, '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': '216.157', 'subgroup_hash': 157, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057399
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 740, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.dr1', 'outer_equivalence': True, 'perfect': False, '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': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 246057400
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 741, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ds1', 'outer_equivalence': True, 'perfect': False, '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': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 246057401
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 742, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.dt1', 'outer_equivalence': True, 'perfect': False, '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': '216.157', 'subgroup_hash': 157, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057402
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 743, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.du1', 'outer_equivalence': True, 'perfect': False, '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': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 246057403
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.dv1', 'outer_equivalence': True, 'perfect': False, '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': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 246057404
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.dw1', 'outer_equivalence': True, 'perfect': False, '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': '216.157', 'subgroup_hash': 157, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057405
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.dx1', 'outer_equivalence': True, 'perfect': False, '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': '216.157', 'subgroup_hash': 157, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057406
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 747, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.dy1', 'outer_equivalence': True, 'perfect': False, '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': '216.157', 'subgroup_hash': 157, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057407
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 27, 'counter': 748, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.dz1', 'outer_equivalence': True, 'perfect': False, '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': '216.102', 'subgroup_hash': 102, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057408
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 27, 'counter': 749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.dz2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.dz2', 'outer_equivalence': True, 'perfect': False, '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': '216.102', 'subgroup_hash': 102, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057410
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ea1', 'outer_equivalence': True, 'perfect': False, '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': '216.37', 'subgroup_hash': 37, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057411
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.eb1', 'outer_equivalence': True, 'perfect': False, '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': '216.51', 'subgroup_hash': 51, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057412
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ec1', 'outer_equivalence': True, 'perfect': False, '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': '216.35', 'subgroup_hash': 35, 'subgroup_order': 216, 'subgroup_tex': '\\He_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246057413
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ed1', 'outer_equivalence': True, 'perfect': False, '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': '216.37', 'subgroup_hash': 37, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057414
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 27, 'counter': 754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ee1', 'outer_equivalence': True, 'perfect': False, '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': '216.50', 'subgroup_hash': 50, 'subgroup_order': 216, 'subgroup_tex': 'C_4\\times C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057415
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 27, 'counter': 755, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ef1', 'outer_equivalence': True, 'perfect': False, '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': '216.50', 'subgroup_hash': 50, 'subgroup_order': 216, 'subgroup_tex': 'C_4\\times C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057416
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 27, 'counter': 756, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.eg1', 'outer_equivalence': True, 'perfect': False, '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': '216.34', 'subgroup_hash': 34, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057417
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 27, 'counter': 757, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.eh1', 'outer_equivalence': True, 'perfect': False, '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': '216.34', 'subgroup_hash': 34, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057418
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 27, 'counter': 758, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ei1', 'outer_equivalence': True, 'perfect': False, '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': '216.102', 'subgroup_hash': 102, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057419
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 759, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ej1', 'outer_equivalence': True, 'perfect': False, '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': '216.51', 'subgroup_hash': 51, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057421
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 760, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ek1', 'outer_equivalence': True, 'perfect': False, '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': '216.35', 'subgroup_hash': 35, 'subgroup_order': 216, 'subgroup_tex': '\\He_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246057422
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 761, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.el1', 'outer_equivalence': True, 'perfect': False, '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': '216.37', 'subgroup_hash': 37, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057423
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 762, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.em1', 'outer_equivalence': True, 'perfect': False, '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': '216.68', 'subgroup_hash': 68, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057424
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 27, 'counter': 763, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.en1', 'outer_equivalence': True, 'perfect': False, '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': '216.67', 'subgroup_hash': 67, 'subgroup_order': 216, 'subgroup_tex': 'C_4\\times C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057425
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 27, 'counter': 764, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.eo1', 'outer_equivalence': True, 'perfect': False, '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': '216.67', 'subgroup_hash': 67, 'subgroup_order': 216, 'subgroup_tex': 'C_4\\times C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057426
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 27, 'counter': 765, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ep1', 'outer_equivalence': True, 'perfect': False, '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': '216.36', 'subgroup_hash': 36, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057427
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 766, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.eq1', 'outer_equivalence': True, 'perfect': False, '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': '216.68', 'subgroup_hash': 68, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057428
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.er1', 'outer_equivalence': True, 'perfect': False, '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': '216.37', 'subgroup_hash': 37, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057429
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 768, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.es1', 'outer_equivalence': True, 'perfect': False, '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': '216.51', 'subgroup_hash': 51, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057430
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 769, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.et1', 'outer_equivalence': True, 'perfect': False, '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': '216.35', 'subgroup_hash': 35, 'subgroup_order': 216, 'subgroup_tex': '\\He_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246057432
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 770, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.eu1', 'outer_equivalence': True, 'perfect': False, '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': '216.68', 'subgroup_hash': 68, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057433
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 771, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ev1', 'outer_equivalence': True, 'perfect': False, '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': '216.166', 'subgroup_hash': 166, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057434
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 772, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ew1', 'outer_equivalence': True, 'perfect': False, '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': '216.164', 'subgroup_hash': 164, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057435
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 773, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ex1', 'outer_equivalence': True, 'perfect': False, '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': '216.92', 'subgroup_hash': 92, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057436
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 774, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ey1', 'outer_equivalence': True, 'perfect': False, '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': '216.60', 'subgroup_hash': 60, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057437
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 775, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ez1', 'outer_equivalence': True, 'perfect': False, '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': '216.167', 'subgroup_hash': 167, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057438
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 776, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.fa1', 'outer_equivalence': True, 'perfect': False, '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': '216.99', 'subgroup_hash': 99, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057439
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 27, 'counter': 777, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.fb1', 'outer_equivalence': True, 'perfect': False, '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': '216.110', 'subgroup_hash': 110, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057440
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 778, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.fc1', 'outer_equivalence': True, 'perfect': False, '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': '216.165', 'subgroup_hash': 165, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057441
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 779, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.fd1', 'outer_equivalence': True, 'perfect': False, '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': '216.166', 'subgroup_hash': 166, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057443
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 780, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.fe1', 'outer_equivalence': True, 'perfect': False, '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': '216.166', 'subgroup_hash': 166, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057444
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 781, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ff1', 'outer_equivalence': True, 'perfect': False, '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': '216.164', 'subgroup_hash': 164, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057445
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 782, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.fg1', 'outer_equivalence': True, 'perfect': False, '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': '216.95', 'subgroup_hash': 95, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057446
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 783, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.fh1', 'outer_equivalence': True, 'perfect': False, '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': '216.72', 'subgroup_hash': 72, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057447
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 784, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.fi1', 'outer_equivalence': True, 'perfect': False, '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': '216.164', 'subgroup_hash': 164, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057448
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 785, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.fj1', 'outer_equivalence': True, 'perfect': False, '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': '216.95', 'subgroup_hash': 95, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057449
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 27, 'counter': 786, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.fk1', 'outer_equivalence': True, 'perfect': False, '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': '216.113', 'subgroup_hash': 113, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057450
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 787, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.fl1', 'outer_equivalence': True, 'perfect': False, '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': '216.164', 'subgroup_hash': 164, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057451
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 788, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.fm1', 'outer_equivalence': True, 'perfect': False, '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': '216.92', 'subgroup_hash': 92, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057452
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 789, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.fn1', 'outer_equivalence': True, 'perfect': False, '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': '216.60', 'subgroup_hash': 60, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057454
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 790, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.fo1', 'outer_equivalence': True, 'perfect': False, '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': '216.165', 'subgroup_hash': 165, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057455
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 791, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.fp1', 'outer_equivalence': True, 'perfect': False, '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': '216.164', 'subgroup_hash': 164, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057456
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 792, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.fq1', 'outer_equivalence': True, 'perfect': False, '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': '216.95', 'subgroup_hash': 95, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057457
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 793, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.fr1', 'outer_equivalence': True, 'perfect': False, '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': '216.72', 'subgroup_hash': 72, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057458
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 794, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.fs1', 'outer_equivalence': True, 'perfect': False, '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': '216.164', 'subgroup_hash': 164, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057459
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 795, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ft1', 'outer_equivalence': True, 'perfect': False, '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': '216.95', 'subgroup_hash': 95, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057460
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 796, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.fu1', 'outer_equivalence': True, 'perfect': False, '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': '216.77', 'subgroup_hash': 77, 'subgroup_order': 216, 'subgroup_tex': 'D_4\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057461
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 797, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.fv1', 'outer_equivalence': True, 'perfect': False, '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': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 246057462
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 798, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.fw1', 'outer_equivalence': True, 'perfect': False, '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': '216.157', 'subgroup_hash': 157, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057463
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 799, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.fx1', 'outer_equivalence': True, 'perfect': False, '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': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 246057466
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 800, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.fy1', 'outer_equivalence': True, 'perfect': False, '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': '216.159', 'subgroup_hash': 159, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246057467
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 801, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.fz1', 'outer_equivalence': True, 'perfect': False, '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': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 246057468
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 802, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ga1', 'outer_equivalence': True, 'perfect': False, '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': '216.159', 'subgroup_hash': 159, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246057469
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 803, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.gb1', 'outer_equivalence': True, 'perfect': False, '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': '216.159', 'subgroup_hash': 159, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246057470
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 804, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.gc1', 'outer_equivalence': True, 'perfect': False, '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': '216.159', 'subgroup_hash': 159, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246057471
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 805, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.gd1', 'outer_equivalence': True, 'perfect': False, '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': '216.157', 'subgroup_hash': 157, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057472
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 806, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ge1', 'outer_equivalence': True, 'perfect': False, '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': '216.159', 'subgroup_hash': 159, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246057473
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 807, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.gf1', 'outer_equivalence': True, 'perfect': False, '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': '216.159', 'subgroup_hash': 159, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246057474
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 808, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.gg1', 'outer_equivalence': True, 'perfect': False, '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': '216.163', 'subgroup_hash': 163, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057475
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 809, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.360.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.gh1', 'outer_equivalence': True, 'perfect': False, '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': '216.163', 'subgroup_hash': 163, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057477
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 810, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.405.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '405.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 405, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1537', 'subgroup_hash': 1537, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057478
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 811, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.405.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '405.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 405, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1514', 'subgroup_hash': 1514, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 246057479
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 812, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.405.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '405.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 405, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1514', 'subgroup_hash': 1514, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 246057480
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 813, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.432.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.26', 'subgroup_hash': 26, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057481
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 814, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.432.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.29', 'subgroup_hash': 29, 'subgroup_order': 180, 'subgroup_tex': 'S_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 246057482
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 815, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.432.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.27', 'subgroup_hash': 27, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057483
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 816, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.432.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.30', 'subgroup_hash': 30, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057484
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 18, 'counter': 817, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.432.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.28', 'subgroup_hash': 28, 'subgroup_order': 180, 'subgroup_tex': 'C_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057485
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 818, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.432.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.26', 'subgroup_hash': 26, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057486
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 819, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.432.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.26', 'subgroup_hash': 26, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057488
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 820, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.432.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.29', 'subgroup_hash': 29, 'subgroup_order': 180, 'subgroup_tex': 'S_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 246057489
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 821, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.432.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.20', 'subgroup_hash': 20, 'subgroup_order': 180, 'subgroup_tex': 'C_3^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246057490
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 822, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.432.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.21', 'subgroup_hash': 21, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057491
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 823, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.432.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.22', 'subgroup_hash': 22, 'subgroup_order': 180, 'subgroup_tex': 'C_3^2:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246057492
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 824, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.432.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.21', 'subgroup_hash': 21, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057493
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 825, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.432.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.20', 'subgroup_hash': 20, 'subgroup_order': 180, 'subgroup_tex': 'C_3^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246057494
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 826, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.432.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.21', 'subgroup_hash': 21, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057495
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 827, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.432.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.19', 'subgroup_hash': 19, 'subgroup_order': 180, 'subgroup_tex': '\\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 246057496
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 828, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.432.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.19', 'subgroup_hash': 19, 'subgroup_order': 180, 'subgroup_tex': '\\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 246057497
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 829, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.432.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.19', 'subgroup_hash': 19, 'subgroup_order': 180, 'subgroup_tex': '\\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 246057499
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 830, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.a1', 'outer_equivalence': True, 'perfect': False, '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': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057500
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 18, 'counter': 831, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.b1', 'outer_equivalence': True, 'perfect': False, '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': '162.34', 'subgroup_hash': 34, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057501
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 18, 'counter': 832, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.c1', 'outer_equivalence': True, 'perfect': False, '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': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 246057502
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 833, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.d1', 'outer_equivalence': True, 'perfect': False, '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': '162.34', 'subgroup_hash': 34, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057503
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 834, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.e1', 'outer_equivalence': True, 'perfect': False, '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': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057504
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 835, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.f1', 'outer_equivalence': True, 'perfect': False, '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': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057505
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 54, 'counter': 836, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.g1', 'outer_equivalence': True, 'perfect': False, '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': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057506
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 837, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.h1', 'outer_equivalence': True, 'perfect': False, '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': '162.48', 'subgroup_hash': 48, 'subgroup_order': 162, 'subgroup_tex': 'C_6\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057507
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 838, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.i1', 'outer_equivalence': True, 'perfect': False, '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': '162.35', 'subgroup_hash': 35, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057508
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 839, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.j1', 'outer_equivalence': True, 'perfect': False, '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': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057510
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 840, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.k1', 'outer_equivalence': True, 'perfect': False, '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': '162.35', 'subgroup_hash': 35, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057511
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 841, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.l1', 'outer_equivalence': True, 'perfect': False, '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': '162.35', 'subgroup_hash': 35, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057512
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 842, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.m1', 'outer_equivalence': True, 'perfect': False, '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': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246057513
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 843, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.n1', 'outer_equivalence': True, 'perfect': False, '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': '162.35', 'subgroup_hash': 35, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057514
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 844, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.o1', 'outer_equivalence': True, 'perfect': False, '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': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 246057515
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 845, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.p1', 'outer_equivalence': True, 'perfect': False, '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': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 246057516
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 846, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.q1', 'outer_equivalence': True, 'perfect': False, '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': '162.34', 'subgroup_hash': 34, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057517
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 847, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.r1', 'outer_equivalence': True, 'perfect': False, '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': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 246057518
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 848, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.s1', 'outer_equivalence': True, 'perfect': False, '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': '162.34', 'subgroup_hash': 34, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057519
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 849, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.t1', 'outer_equivalence': True, 'perfect': False, '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': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057521
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 850, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.u1', 'outer_equivalence': True, 'perfect': False, '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': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057522
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 851, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.v1', 'outer_equivalence': True, 'perfect': False, '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': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057523
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 852, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.w1', 'outer_equivalence': True, 'perfect': False, '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': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057524
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 853, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.x1', 'outer_equivalence': True, 'perfect': False, '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': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 246057525
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 854, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.y1', 'outer_equivalence': True, 'perfect': False, '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': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057526
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 855, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.z1', 'outer_equivalence': True, 'perfect': False, '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': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057527
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 856, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.ba1', 'outer_equivalence': True, 'perfect': False, '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': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 246057528
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 857, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.bb1', 'outer_equivalence': True, 'perfect': False, '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': '162.46', 'subgroup_hash': 46, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057529
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 858, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.bc1', 'outer_equivalence': True, 'perfect': False, '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': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057530
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 859, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.bd1', 'outer_equivalence': True, 'perfect': False, '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': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057532
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 860, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.be1', 'outer_equivalence': True, 'perfect': False, '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': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057533
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 861, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.bf1', 'outer_equivalence': True, 'perfect': False, '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': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057534
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 862, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.bg1', 'outer_equivalence': True, 'perfect': False, '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': '162.46', 'subgroup_hash': 46, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057535
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 863, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.bh1', 'outer_equivalence': True, 'perfect': False, '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': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057536
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 864, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.bi1', 'outer_equivalence': True, 'perfect': False, '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': '162.46', 'subgroup_hash': 46, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057537
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 865, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.bj1', 'outer_equivalence': True, 'perfect': False, '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': '162.46', 'subgroup_hash': 46, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246057538
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 866, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.480.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.bk1', 'outer_equivalence': True, 'perfect': False, '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': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057539
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 867, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.193', 'subgroup_hash': 193, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2:C_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057540
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 868, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057541
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 869, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.186', 'subgroup_hash': 186, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057543
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 870, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.186', 'subgroup_hash': 186, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057544
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 871, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057545
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 872, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057546
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 873, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057547
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 874, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.186', 'subgroup_hash': 186, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057548
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 875, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057549
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 876, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057550
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 877, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.191', 'subgroup_hash': 191, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057551
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 878, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.159', 'subgroup_hash': 159, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057552
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 879, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.146', 'subgroup_hash': 146, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057554
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 880, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057555
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 881, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057556
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 882, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057557
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 883, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.p2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.p2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057558
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 884, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057559
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 885, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057560
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 886, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.195', 'subgroup_hash': 195, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057561
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 887, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057562
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 888, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057563
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 889, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057565
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 890, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057566
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 891, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057567
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 892, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057568
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 893, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057569
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 894, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057570
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 895, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057571
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 896, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057572
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 897, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057573
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 898, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057574
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 899, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057577
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 900, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057578
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 901, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057579
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 902, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057580
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 903, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057581
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 904, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057582
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 905, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057583
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 906, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057584
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 907, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057585
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 908, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057586
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 909, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057588
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 910, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057589
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 911, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057590
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 912, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057591
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 913, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057592
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 914, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057593
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 915, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.169', 'subgroup_hash': 169, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057594
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 916, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.149', 'subgroup_hash': 149, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057595
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 917, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057596
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 918, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057597
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 919, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057599
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 920, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.bz2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bz2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057600
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 921, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057601
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 922, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057602
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 923, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057603
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 924, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057604
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 925, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057605
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 926, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.145', 'subgroup_hash': 145, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057606
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 927, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.145', 'subgroup_hash': 145, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057607
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 928, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.145', 'subgroup_hash': 145, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057608
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 929, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057610
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 930, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057611
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 931, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057612
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 932, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057613
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 933, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057614
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 934, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.cm2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.cm2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057615
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 935, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057616
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 936, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057617
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 937, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057618
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 938, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.193', 'subgroup_hash': 193, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2:C_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057619
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 939, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057621
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 940, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.186', 'subgroup_hash': 186, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057622
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 941, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.186', 'subgroup_hash': 186, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057623
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 942, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057624
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 943, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057625
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 944, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057626
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 945, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.186', 'subgroup_hash': 186, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 246057627
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 946, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057628
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 947, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057629
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 948, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.cz2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.cz2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057630
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 949, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057632
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 950, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057633
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 951, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.159', 'subgroup_hash': 159, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057634
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 952, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.146', 'subgroup_hash': 146, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057635
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 953, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.159', 'subgroup_hash': 159, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057636
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 954, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057637
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 955, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057638
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 956, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057639
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 957, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057640
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 958, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.195', 'subgroup_hash': 195, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057641
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 959, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.195', 'subgroup_hash': 195, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057643
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 960, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057644
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 961, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057645
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 962, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057646
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 963, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057647
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 964, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057648
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 965, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057649
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 966, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057650
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 967, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057651
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 968, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057652
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 969, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057654
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 970, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057655
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 971, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 246057656
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 972, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057657
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 973, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057658
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 974, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057659
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 975, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246057660
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 976, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057661
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 977, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057662
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 978, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057663
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 979, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057665
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 980, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057666
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 981, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057667
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 982, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246057668
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 983, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.150', 'subgroup_hash': 150, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057669
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 984, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057670
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 985, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057671
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 986, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.160', 'subgroup_hash': 160, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057672
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 987, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057673
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 988, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057674
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 989, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057676
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 990, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057677
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 991, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057678
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 992, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057679
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 993, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.170', 'subgroup_hash': 170, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057680
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 994, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.160', 'subgroup_hash': 160, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057681
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 995, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.160', 'subgroup_hash': 160, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246057682
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 996, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057683
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 997, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057684
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 998, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246057685
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 999, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054840
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1000, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054841
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1001, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054842
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1002, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054843
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1003, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054844
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1004, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054845
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1005, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054846
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1006, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054847
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1007, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.177', 'subgroup_hash': 177, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054848
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1008, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1009, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1010, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054852
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1011, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054853
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1012, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054854
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1013, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054855
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1014, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054856
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1015, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054857
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1016, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054858
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1017, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054859
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1018, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054860
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1019, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054862
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1020, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054863
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1021, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054864
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1022, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054865
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1023, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054866
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1024, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054867
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1025, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '540.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.179', 'subgroup_hash': 179, 'subgroup_order': 144, 'subgroup_tex': 'C_4:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054868
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1026, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '540.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.179', 'subgroup_hash': 179, 'subgroup_order': 144, 'subgroup_tex': 'C_4:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054869
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 1027, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054870
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1028, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054871
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1029, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054873
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1030, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246054874
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1031, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246054875
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1032, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.145', 'subgroup_hash': 145, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054876
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1033, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.145', 'subgroup_hash': 145, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054877
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1034, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246054878
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1035, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246054879
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1036, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.145', 'subgroup_hash': 145, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054880
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1037, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246054881
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1038, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246054882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1039, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054884
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1040, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054885
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1041, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054886
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1042, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054887
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1043, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1044, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054889
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1045, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054890
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1046, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054891
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1047, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054892
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1048, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054893
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1049, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054895
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1050, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054896
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1051, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054897
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1052, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054898
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1053, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ha1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054899
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1054, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.hb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054900
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1055, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.hc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054901
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1056, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.hd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054902
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1057, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.he1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054903
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1058, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.hf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054904
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1059, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.hg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054906
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1060, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.hh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054907
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1061, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.hi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054908
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1062, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.hj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054909
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1063, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.hk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054910
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1064, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.hl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054911
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1065, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.hm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054912
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1066, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.hn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054913
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1067, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.540.ho1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246054914
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 27, 'counter': 1068, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.576.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '135.3', 'subgroup_hash': 3, 'subgroup_order': 135, 'subgroup_tex': 'C_5\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246054915
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1069, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.648.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.40', 'subgroup_hash': 40, 'subgroup_order': 120, 'subgroup_tex': 'C_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246054917
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1070, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.648.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.41', 'subgroup_hash': 41, 'subgroup_order': 120, 'subgroup_tex': 'C_{30}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246054918
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1071, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.648.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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: 246054919
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1072, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.648.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246054920
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1073, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.648.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246054921
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1074, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.648.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246054922
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1075, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.648.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246054923
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1076, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.648.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 246054924
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1077, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.648.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 246054925
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1078, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.648.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.40', 'subgroup_hash': 40, 'subgroup_order': 120, 'subgroup_tex': 'C_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246054926
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1079, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.648.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.41', 'subgroup_hash': 41, 'subgroup_order': 120, 'subgroup_tex': 'C_{30}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246054928
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1080, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.648.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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: 246054929
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1081, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.648.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246054930
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1082, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.648.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246054931
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1083, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.648.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246054932
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 1084, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.648.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '120.34', 'subgroup_hash': 34, 'subgroup_order': 120, 'subgroup_tex': 'S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246054933
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1085, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.648.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '120.34', 'subgroup_hash': 34, 'subgroup_order': 120, 'subgroup_tex': 'S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246054934
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1086, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.648.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '120.34', 'subgroup_hash': 34, 'subgroup_order': 120, 'subgroup_tex': 'S_5', 'supersolvable': False, 'sylow': 0}
  • id: 246054935
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': True, 'centralizer_order': 720, 'characteristic': True, 'core_order': 108, 'counter': 1087, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '77760.bo.720.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '720.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '720.763', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 763, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 720, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'S_6', 'simple': False, 'solvable': True, 'special_labels': ['R', 'C2', 'R', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054936
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1088, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.b1', 'outer_equivalence': True, 'perfect': False, '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': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054937
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1089, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.c1', 'outer_equivalence': True, 'perfect': False, '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': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054939
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1090, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.d1', 'outer_equivalence': True, 'perfect': False, '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': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054940
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1091, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.e1', 'outer_equivalence': True, 'perfect': False, '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': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054941
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1092, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.f1', 'outer_equivalence': True, 'perfect': False, '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': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054942
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1093, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.g1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054943
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 1094, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.h1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054944
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1095, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.i1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054945
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1096, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.j1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054946
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1097, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.k1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054947
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1098, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.l1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054948
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1099, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.m1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054951
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.n1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054952
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.o1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054953
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.p1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054954
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.q1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054955
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.r1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054956
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.s1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054957
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.t1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054958
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 1107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.u1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054959
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.v1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054960
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.w1', 'outer_equivalence': True, 'perfect': False, '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': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054962
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.x1', 'outer_equivalence': True, 'perfect': False, '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': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054963
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 1111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.y1', 'outer_equivalence': True, 'perfect': False, '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': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054964
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 1112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.z1', 'outer_equivalence': True, 'perfect': False, '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': '108.25', 'subgroup_hash': 25, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054965
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 54, 'counter': 1113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.ba1', 'outer_equivalence': True, 'perfect': False, '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': '108.25', 'subgroup_hash': 25, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054966
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 1114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.bb1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054967
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 54, 'counter': 1115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.bc1', 'outer_equivalence': True, 'perfect': False, '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': '108.25', 'subgroup_hash': 25, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054968
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 1116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.bd1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054969
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 1117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.be1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054970
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 1118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.bf1', 'outer_equivalence': True, 'perfect': False, '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': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054971
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 1119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.bg1', 'outer_equivalence': True, 'perfect': False, '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': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054973
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 54, 'counter': 1120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.bh1', 'outer_equivalence': True, 'perfect': False, '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': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054974
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 1121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.bi1', 'outer_equivalence': True, 'perfect': False, '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': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054975
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 1122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.bj1', 'outer_equivalence': True, 'perfect': False, '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': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054976
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 54, 'counter': 1123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.bk1', 'outer_equivalence': True, 'perfect': False, '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': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054977
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 1124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.bl1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054978
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.bm1', 'outer_equivalence': True, 'perfect': False, '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': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054979
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.bn1', 'outer_equivalence': True, 'perfect': False, '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': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054980
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.bo1', 'outer_equivalence': True, 'perfect': False, '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': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054981
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.bp1', 'outer_equivalence': True, 'perfect': False, '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': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054982
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.bq1', 'outer_equivalence': True, 'perfect': False, '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': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054984
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.br1', 'outer_equivalence': True, 'perfect': False, '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': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246054985
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.bs1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054986
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.bt1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054987
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.bu1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054988
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.bv1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054989
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.bw1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054990
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.bx1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054991
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.by1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054992
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.bz1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054993
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.ca1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054995
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.cb1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054996
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.cc1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054997
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.cd1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054998
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.ce1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246054999
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.cf1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055000
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.cg1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055001
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.ch1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055002
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.ci1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055003
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 54, 'counter': 1148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.cj1', 'outer_equivalence': True, 'perfect': False, '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': '108.28', 'subgroup_hash': 28, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055004
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 54, 'counter': 1149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.ck1', 'outer_equivalence': True, 'perfect': False, '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': '108.28', 'subgroup_hash': 28, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055006
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 54, 'counter': 1150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.cl1', 'outer_equivalence': True, 'perfect': False, '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': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055007
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 54, 'counter': 1151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.cm1', 'outer_equivalence': True, 'perfect': False, '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': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055008
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.cn1', 'outer_equivalence': True, 'perfect': False, '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': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055009
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.co1', 'outer_equivalence': True, 'perfect': False, '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': '108.25', 'subgroup_hash': 25, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055010
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 27, 'counter': 1154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.cp1', 'outer_equivalence': True, 'perfect': False, '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': '108.25', 'subgroup_hash': 25, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055011
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 1155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.cp2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.cp2', 'outer_equivalence': True, 'perfect': False, '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': '108.25', 'subgroup_hash': 25, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055012
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.cq1', 'outer_equivalence': True, 'perfect': False, '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': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055013
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.cr1', 'outer_equivalence': True, 'perfect': False, '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': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055014
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.cs1', 'outer_equivalence': True, 'perfect': False, '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': '108.28', 'subgroup_hash': 28, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055015
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 27, 'counter': 1159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.ct1', 'outer_equivalence': True, 'perfect': False, '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': '108.28', 'subgroup_hash': 28, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055017
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 27, 'counter': 1160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.ct2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.ct2', 'outer_equivalence': True, 'perfect': False, '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': '108.28', 'subgroup_hash': 28, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055018
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.cu1', 'outer_equivalence': True, 'perfect': False, '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': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055019
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.cv1', 'outer_equivalence': True, 'perfect': False, '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': '108.28', 'subgroup_hash': 28, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 27, 'counter': 1163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.cw1', 'outer_equivalence': True, 'perfect': False, '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': '108.30', 'subgroup_hash': 30, 'subgroup_order': 108, 'subgroup_tex': 'C_2^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 27, 'counter': 1164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.cw2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.cw2', 'outer_equivalence': True, 'perfect': False, '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': '108.30', 'subgroup_hash': 30, 'subgroup_order': 108, 'subgroup_tex': 'C_2^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055022
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.cx1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055023
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.cy1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055024
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.cz1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055025
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.da1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055026
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 1169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.db1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055028
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.dc1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055029
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.dd1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055030
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.de1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055031
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.df1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055032
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.dg1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055033
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.dh1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055034
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.di1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055035
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.dj1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055036
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.dk1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055037
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.dl1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055039
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.dm1', 'outer_equivalence': True, 'perfect': False, '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': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055040
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.dn1', 'outer_equivalence': True, 'perfect': False, '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': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055041
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 1182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.do1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055042
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.dp1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055043
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.dq1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055044
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 27, 'counter': 1185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.dr1', 'outer_equivalence': True, 'perfect': False, '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': '108.25', 'subgroup_hash': 25, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055045
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 1186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.dr2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.dr2', 'outer_equivalence': True, 'perfect': False, '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': '108.25', 'subgroup_hash': 25, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055046
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 27, 'counter': 1187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.ds1', 'outer_equivalence': True, 'perfect': False, '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': '108.28', 'subgroup_hash': 28, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055047
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 27, 'counter': 1188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.ds2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.ds2', 'outer_equivalence': True, 'perfect': False, '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': '108.28', 'subgroup_hash': 28, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055048
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 27, 'counter': 1189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.dt1', 'outer_equivalence': True, 'perfect': False, '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': '108.25', 'subgroup_hash': 25, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055050
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 27, 'counter': 1190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.du1', 'outer_equivalence': True, 'perfect': False, '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': '108.28', 'subgroup_hash': 28, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055051
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 27, 'counter': 1191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.dv1', 'outer_equivalence': True, 'perfect': False, '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': '108.13', 'subgroup_hash': 13, 'subgroup_order': 108, 'subgroup_tex': 'C_4\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055052
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 27, 'counter': 1192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.dw1', 'outer_equivalence': True, 'perfect': False, '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': '108.13', 'subgroup_hash': 13, 'subgroup_order': 108, 'subgroup_tex': 'C_4\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 27, 'counter': 1193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.dx1', 'outer_equivalence': True, 'perfect': False, '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': '108.11', 'subgroup_hash': 11, 'subgroup_order': 108, 'subgroup_tex': '\\He_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 27, 'counter': 1194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.dy1', 'outer_equivalence': True, 'perfect': False, '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': '108.8', 'subgroup_hash': 8, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055055
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 27, 'counter': 1195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.dz1', 'outer_equivalence': True, 'perfect': False, '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': '108.8', 'subgroup_hash': 8, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055056
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 27, 'counter': 1196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.ea1', 'outer_equivalence': True, 'perfect': False, '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': '108.11', 'subgroup_hash': 11, 'subgroup_order': 108, 'subgroup_tex': '\\He_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055057
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.eb1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055058
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.ec1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055059
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.ed1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055062
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.ee1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055063
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.ef1', 'outer_equivalence': True, 'perfect': False, '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': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055064
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.eg1', 'outer_equivalence': True, 'perfect': False, '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': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055065
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 27, 'counter': 1203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.eh1', 'outer_equivalence': True, 'perfect': False, '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': '108.30', 'subgroup_hash': 30, 'subgroup_order': 108, 'subgroup_tex': 'C_2^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055066
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.ei1', 'outer_equivalence': True, 'perfect': False, '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': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055067
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.ej1', 'outer_equivalence': True, 'perfect': False, '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': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055068
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.ek1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055069
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.el1', 'outer_equivalence': True, 'perfect': False, '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': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055070
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.em1', 'outer_equivalence': True, 'perfect': False, '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': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055071
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.en1', 'outer_equivalence': True, 'perfect': False, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055073
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.eo1', 'outer_equivalence': True, 'perfect': False, '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': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055074
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.ep1', 'outer_equivalence': True, 'perfect': False, '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': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055075
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 1212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.eq1', 'outer_equivalence': True, 'perfect': False, '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': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246055076
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.er1', 'outer_equivalence': True, 'perfect': False, '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': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246055077
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.es1', 'outer_equivalence': True, 'perfect': False, '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': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055078
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.et1', 'outer_equivalence': True, 'perfect': False, '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': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246055079
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.eu1', 'outer_equivalence': True, 'perfect': False, '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': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055080
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.ev1', 'outer_equivalence': True, 'perfect': False, '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': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246055081
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.ew1', 'outer_equivalence': True, 'perfect': False, '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': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055082
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.ex1', 'outer_equivalence': True, 'perfect': False, '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': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 246055084
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.ey1', 'outer_equivalence': True, 'perfect': False, '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': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055085
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.ez1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055086
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.fa1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055087
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.fb1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055088
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.fc1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055089
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 1225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.fd1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055090
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.fe1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055091
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.ff1', 'outer_equivalence': True, 'perfect': False, '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': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055092
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.fg1', 'outer_equivalence': True, 'perfect': False, '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': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055093
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 27, 'counter': 1229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.fh1', 'outer_equivalence': True, 'perfect': False, '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': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055095
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 1230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.fh2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.fh2', 'outer_equivalence': True, 'perfect': False, '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': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055096
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.fi1', 'outer_equivalence': True, 'perfect': False, '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': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055097
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.fj1', 'outer_equivalence': True, 'perfect': False, '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': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055098
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.fk1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055099
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.fl1', 'outer_equivalence': True, 'perfect': False, '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': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055100
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.fm1', 'outer_equivalence': True, 'perfect': False, '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': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055101
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 27, 'counter': 1236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.fn1', 'outer_equivalence': True, 'perfect': False, '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': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055102
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 1237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.fn2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.fn2', 'outer_equivalence': True, 'perfect': False, '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': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055103
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 1238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.fo1', 'outer_equivalence': True, 'perfect': False, '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': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055104
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.fp1', 'outer_equivalence': True, 'perfect': False, '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': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055106
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 1240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.fq1', 'outer_equivalence': True, 'perfect': False, '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': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055107
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.fr1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055108
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.fs1', 'outer_equivalence': True, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055109
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 27, 'counter': 1243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.720.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.ft1', 'outer_equivalence': True, 'perfect': False, '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': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055110
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.207', 'subgroup_hash': 207, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055111
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055112
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055113
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.219', 'subgroup_hash': 219, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055114
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055115
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055117
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '810.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.221', 'subgroup_hash': 221, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 246055119
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055120
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055121
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055122
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055123
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055124
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055125
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055126
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055128
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055129
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055130
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055131
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055132
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055133
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055134
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055135
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055136
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055137
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055139
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.206', 'subgroup_hash': 206, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 246055140
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055141
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055142
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.230', 'subgroup_hash': 230, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055143
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055144
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.206', 'subgroup_hash': 206, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 246055145
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055146
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055147
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.230', 'subgroup_hash': 230, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055148
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055150
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.207', 'subgroup_hash': 207, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055152
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055153
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.219', 'subgroup_hash': 219, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055154
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055155
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055156
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055157
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '810.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.221', 'subgroup_hash': 221, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 246055158
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055159
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055161
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055162
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055163
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055164
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055165
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055166
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055167
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055168
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.810.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055169
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 9, 'counter': 1298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.864.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 246055170
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 18, 'counter': 1299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.864.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.8', 'subgroup_hash': 8, 'subgroup_order': 90, 'subgroup_tex': 'C_{15}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055173
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 9, 'counter': 1300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.864.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 246055174
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 3, 'counter': 1301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.864.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 246055175
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 1302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.864.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 246055176
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 1303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.864.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 246055177
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 1304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.864.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 246055178
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 1305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.864.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.9', 'subgroup_hash': 9, 'subgroup_order': 90, 'subgroup_tex': 'C_3:D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 246055179
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 1306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.864.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 246055180
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.864.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 246055181
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 1308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.960.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '960.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 960, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055182
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 1309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.960.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '960.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 960, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 246055184
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 27, 'counter': 1310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.960.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '960.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 960, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055185
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 1311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.960.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '960.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 960, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055186
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 1312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.960.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '960.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 960, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 246055187
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.972.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246055188
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055189
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055190
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055191
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055192
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055193
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055195
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055196
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055197
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055198
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055199
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055200
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055201
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055202
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055203
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055204
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 1329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.o2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.o2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055206
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055207
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055208
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055209
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 1333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.r2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.r2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055210
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055211
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055212
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055213
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055214
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055215
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 1339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.w2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.w2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055217
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055218
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055219
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055220
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055221
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055222
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055223
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055224
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055225
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055226
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055228
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055229
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055230
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055231
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055232
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055233
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055234
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055235
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055236
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 1358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.bo2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bo2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055237
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055239
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 1360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.bp2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bp2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055240
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055241
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 1362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.bq2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bq2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055242
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055243
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055244
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055245
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055246
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055247
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055248
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 18, 'counter': 1369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055250
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 1370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055251
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055252
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055253
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055254
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055255
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055256
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055257
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055258
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055259
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055261
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055262
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055263
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055264
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 1383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ck2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ck2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055265
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055266
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055267
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055268
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 1387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.cn2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.cn2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055269
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055270
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 1389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.co2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.co2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055272
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055273
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055274
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055275
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055276
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 1394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.cs2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.cs2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055277
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055278
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055279
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055280
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055281
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055284
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055285
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055286
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055287
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055288
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055289
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055290
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055291
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055292
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055293
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055295
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.dh2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.dh2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055296
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.dh3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.dh3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055297
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.dh4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.dh4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055298
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055299
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.di2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.di2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055300
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 246055301
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055302
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.dk2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.dk2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055303
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 246055304
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055306
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.dm2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.dm2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055307
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055308
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.dn2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.dn2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055309
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 246055310
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 246055311
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 246055312
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 246055313
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 246055314
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 246055315
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 1429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1080.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055317
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055318
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055319
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055320
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 1433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1080.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055321
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055322
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1080.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055323
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1080.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055324
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1080.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055325
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1080.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055326
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 1439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1080.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055328
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 1440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1080.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055329
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 1441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055330
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055331
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055332
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055333
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055334
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055335
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055336
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 1448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055337
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055339
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055340
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 246055341
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 246055342
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 1453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 246055343
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055344
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.et2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.et2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055345
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.22', 'subgroup_hash': 22, 'subgroup_order': 72, 'subgroup_tex': 'D_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055346
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055347
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055348
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.22', 'subgroup_hash': 22, 'subgroup_order': 72, 'subgroup_tex': 'D_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055350
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055351
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055352
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055353
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055354
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055355
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055356
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.fd2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.fd2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055357
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055358
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055359
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.33', 'subgroup_hash': 33, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055361
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055362
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055363
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055364
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055365
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055366
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055367
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.fm2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.fm2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055368
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055369
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.33', 'subgroup_hash': 33, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055370
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.22', 'subgroup_hash': 22, 'subgroup_order': 72, 'subgroup_tex': 'D_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055372
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055373
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055374
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055375
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055376
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055377
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055378
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055379
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055380
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055381
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055383
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055384
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.22', 'subgroup_hash': 22, 'subgroup_order': 72, 'subgroup_tex': 'D_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055385
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055386
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055387
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055388
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.33', 'subgroup_hash': 33, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055389
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055390
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055391
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055392
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 246055395
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055396
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055397
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055398
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055399
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055400
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055401
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 246055402
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055403
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055404
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055406
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055407
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055408
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055409
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 246055410
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 246055411
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055412
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ha1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055413
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.hb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055414
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.hc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055415
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.hd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055417
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.he1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055418
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.hf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055419
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.hg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055420
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.hh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055421
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.hi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055422
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.hj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055423
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.hk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 246055424
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.hl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055425
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.hm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055426
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.hn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 246055428
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ho1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055429
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.hp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055430
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.hq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055431
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.hr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055432
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.hs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.hs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 246055433
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ht1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ht1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 246055434
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.hu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.hu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055435
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.hv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.hv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055436
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.hw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.hw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055437
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.hx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.hx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055439
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.hy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.hy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055440
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.hz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1080.hz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055441
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ia1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1080.ia1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055442
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ib1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ib1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 246055443
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ic1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ic1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 246055444
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.id1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.id1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 246055445
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ie1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ie1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 246055446
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 1547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.if1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.if1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055447
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ig1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ig1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055448
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1080.ih1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ih1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055450
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1550, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '77760.bo.1215.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1215.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1215, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.261', 'subgroup_hash': 261, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times C_2^3', 'supersolvable': True, 'sylow': 2}
  • id: 246055451
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1296.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 246055452
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1296.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': 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: 246055453
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1296.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 246055454
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1296.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 246055455
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1296.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 246055456
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1296.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 246055457
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 1557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1296.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 246055458
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 3, 'counter': 1558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1296.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 246055459
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1296.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 246055461
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1296.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': 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: 246055462
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1296.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 246055463
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1296.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 246055464
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1296.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 246055465
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 1564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1296.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246055466
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1296.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.7', 'subgroup_hash': 7, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055467
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1296.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246055468
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1296.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246055469
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1296.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246055470
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1296.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.7', 'subgroup_hash': 7, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055472
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1296.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.7', 'subgroup_hash': 7, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055473
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1296.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246055474
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1296.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.7', 'subgroup_hash': 7, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055475
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 1573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1296.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.w1', 'outer_equivalence': True, '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': 1296, '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: 246055476
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 720, 'characteristic': False, 'core_order': 54, 'counter': 1574, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '77760.bo.1440.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1440.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '1440.5842', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5842, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1440, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055477
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2160, 'characteristic': True, 'core_order': 54, 'counter': 1575, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '77760.bo.1440.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1440.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '1440.5842', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5842, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1440, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_6', 'simple': False, 'solvable': True, 'special_labels': ['C3', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055478
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 1576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055479
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 1577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055480
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 1578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055481
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 1579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055483
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055484
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 1581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055485
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 1582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055486
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 1583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055487
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 1584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055488
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 1585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055489
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055490
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 1587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055491
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055492
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055494
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 1590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055495
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055496
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 27, 'counter': 1592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055497
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 1593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055498
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055499
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 1595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055500
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 1596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055501
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 1597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055502
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 1598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055503
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 1599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055506
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055507
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 1601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055508
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055509
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055510
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 27, 'counter': 1604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055511
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055512
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055513
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 1607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055514
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055515
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055517
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055518
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055519
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055520
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055521
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055522
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055523
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055524
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 27, 'counter': 1617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055525
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055526
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 1619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055528
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055529
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055530
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055531
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055532
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055533
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055534
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055535
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 1627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055536
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 1628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055537
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055539
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055540
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055541
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 27, 'counter': 1632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055542
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055543
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055544
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055545
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055546
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055547
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055548
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055550
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055551
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 1641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055552
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055553
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055554
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055555
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 1645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055556
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055557
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055558
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055559
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055561
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055562
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 27, 'counter': 1651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055563
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055564
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055565
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055566
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055567
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055568
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055569
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 1658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.df2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.df2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055570
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055572
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1440.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055573
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055574
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 246055575
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055576
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055577
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055578
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.e2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.e2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055579
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055580
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055581
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.52', 'subgroup_hash': 52, 'subgroup_order': 48, 'subgroup_tex': 'C_2^3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055583
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055584
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055585
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055586
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055587
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055588
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055589
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1676, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055590
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1677, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055591
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1678, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055592
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1679, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055594
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055595
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055596
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055597
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055598
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055599
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055600
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055601
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055602
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055603
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055605
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 1690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055606
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055607
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055608
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055609
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055610
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055611
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055612
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055613
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.bj2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.bj2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055614
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055617
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055618
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.bl2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.bl2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055619
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055620
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055621
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055622
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055623
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 1706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055624
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055625
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055626
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055628
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1710, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055629
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1711, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055630
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055631
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055632
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055633
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055634
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055635
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055636
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055637
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055639
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055640
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055641
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1722, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055642
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1723, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055643
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055644
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055645
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055646
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ck2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ck2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055647
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055648
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055650
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1730, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055651
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055652
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 1732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.co2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.co2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055653
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055654
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1734, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055655
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1735, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055656
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1736, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055657
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1737, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.cs2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.cs2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055658
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055659
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1739, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055661
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 1740, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055662
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1741, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 246055663
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1742, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055664
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1743, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055665
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 1744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.52', 'subgroup_hash': 52, 'subgroup_order': 48, 'subgroup_tex': 'C_2^3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055666
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055667
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055668
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1747, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055669
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1748, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055670
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055672
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055673
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055674
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055675
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055676
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055677
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1755, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055678
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1756, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055679
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1757, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055680
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1758, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055681
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1759, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055683
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1760, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055684
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1761, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055685
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1762, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055686
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1763, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055687
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1764, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ds2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ds2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055688
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1765, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055689
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1766, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055690
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055691
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1768, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055692
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1769, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055694
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1770, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055695
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1771, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055696
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1772, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055697
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1773, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055698
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1774, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055699
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1775, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055700
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1776, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055701
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1777, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055702
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1778, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055703
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1779, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055705
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1780, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055706
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1781, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055707
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1782, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246055708
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1783, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055709
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1784, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055710
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1785, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055711
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1786, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055712
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1787, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055713
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1788, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055714
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1789, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055716
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1790, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055717
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1791, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.es2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.es2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055718
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1792, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055719
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1793, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055720
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1794, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055721
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1795, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055722
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1796, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055723
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1797, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055724
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1798, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055725
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1799, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055728
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1800, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055729
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1801, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055730
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1802, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055731
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1803, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055732
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1804, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055733
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1805, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055734
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1806, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055735
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1807, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1808, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055737
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1809, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055739
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1810, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1811, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055741
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1812, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055742
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1813, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055743
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1814, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055744
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1815, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055745
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1816, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055746
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1817, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1818, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055748
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1819, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055750
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1820, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055751
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1821, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055752
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1822, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055753
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1823, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055754
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1824, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055755
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1825, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055756
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1826, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055757
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1827, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055758
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1828, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055759
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1829, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055761
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1830, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055762
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1831, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 1832, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 1833, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055765
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1834, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 1835, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055767
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1836, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055768
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1837, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055769
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1838, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055770
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1839, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055772
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1840, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055773
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1841, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055774
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1842, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055775
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1843, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055776
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1844, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055777
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1845, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055778
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1846, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055779
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1847, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055780
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1848, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055781
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1849, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055783
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1850, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055784
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1851, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ha1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055785
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1852, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.hb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055786
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1853, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.hc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055787
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1854, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.hd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055788
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1855, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.he1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055789
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1856, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.hf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055790
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1857, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.hg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055791
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1858, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.hh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055792
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1859, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.hi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055794
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1860, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.hj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055795
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1861, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.hk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1862, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.hl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055797
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1863, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.hm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055798
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 1864, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.hn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055799
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1865, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ho1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055800
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1866, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.hp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055801
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1867, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.hq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055802
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1868, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.hr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055803
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1869, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.hs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.hs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055805
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1870, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.ht1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.ht1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055806
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1871, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.hu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.hu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1872, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1620.hv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.hv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055808
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 9, 'counter': 1873, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1728.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 246055809
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 3, 'counter': 1874, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1728.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 246055810
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1875, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1944.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246055811
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1876, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1944.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246055812
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1877, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1944.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 246055813
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1878, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1944.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246055814
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1879, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.1944.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246055816
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1880, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055817
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1881, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055818
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1882, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055819
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1883, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055820
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1884, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055821
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1885, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055822
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1886, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055823
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1887, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055824
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1888, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055825
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1889, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055827
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1890, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055828
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1891, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055829
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1892, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055830
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1893, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055831
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 9, 'counter': 1894, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055832
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1895, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055833
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 1896, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055834
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1897, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055835
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1898, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055836
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1899, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055839
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 1900, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055840
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1901, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055841
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1902, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055842
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1903, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055843
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1904, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055844
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1905, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055845
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 1906, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055846
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1907, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055847
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1908, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055848
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1909, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055850
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 1910, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055851
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1911, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055852
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1912, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055853
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1913, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055854
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1914, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055855
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 18, 'counter': 1915, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055856
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 1916, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055857
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 18, 'counter': 1917, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055858
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 1918, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055859
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 720, 'characteristic': False, 'core_order': 18, 'counter': 1919, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055861
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1920, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055862
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 1921, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055863
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1922, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055864
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1923, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055865
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1924, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055866
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1925, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055867
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1926, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055868
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1927, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055869
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1928, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055870
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1929, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055872
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 1930, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055873
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1931, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055874
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1932, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055875
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 9, 'counter': 1933, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055876
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 1934, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055877
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1935, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055878
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1936, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055879
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1937, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055880
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1938, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055881
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1939, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055883
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1940, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055884
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 1941, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055885
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 1942, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055886
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1943, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055887
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1944, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055888
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1945, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055889
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 1946, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055890
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1947, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055891
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1948, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055892
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 1949, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055894
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1950, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055895
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1951, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055896
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1952, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055897
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 1953, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.cu2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.cu2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055898
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1954, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055899
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1955, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055900
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1956, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055901
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 1957, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.cx2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.cx2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055902
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1958, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055903
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 1959, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055905
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1960, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055906
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1961, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055907
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1962, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055908
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 1963, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.dc2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.dc2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055909
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1964, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055910
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 1965, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.dd2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.dd2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055911
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1966, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055912
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1967, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055913
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 1968, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055914
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1969, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055916
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1970, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055917
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 1971, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055918
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 9, 'counter': 1972, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.dj2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.dj2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055919
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 1973, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055920
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 1974, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.dk2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.dk2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055921
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1975, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055922
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1976, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055923
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1977, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055924
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1978, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055925
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1979, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055927
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1980, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055928
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 1981, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055929
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1982, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055930
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1983, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055931
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1984, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055932
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1985, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055933
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1986, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055934
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 1987, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055935
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1988, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055936
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1989, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055938
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 1990, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055939
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1991, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055940
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 1992, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.eb2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.eb2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055941
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1993, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055942
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 1994, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ec2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ec2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055943
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1995, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055944
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 1996, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ed2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ed2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055945
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 1997, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055946
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 1998, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ee2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ee2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055947
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 1999, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055951
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2000, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055952
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 2001, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055953
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2002, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055954
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 2003, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055955
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 2004, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055956
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 2005, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055957
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 2006, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055958
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2007, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055959
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 2008, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055960
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2009, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246055962
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 2010, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055963
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2011, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055964
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2012, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055965
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2013, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055966
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2014, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246055967
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2015, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055968
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2016, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055969
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2017, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055970
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2018, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055971
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2019, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055973
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2020, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055974
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 2021, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055975
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 2022, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055976
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 2023, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055977
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2024, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055978
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2025, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055979
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2026, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055980
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2027, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055981
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2028, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055982
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2029, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055984
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2030, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055985
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2031, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055986
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2032, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055987
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2033, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055988
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2034, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 246055989
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2035, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246055990
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2036, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055991
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 2037, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.fq2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.fq2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055992
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2038, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055993
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 2039, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055995
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2040, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055996
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2041, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055997
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2042, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055998
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2043, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246055999
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2044, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056000
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2045, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056001
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2046, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056002
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2047, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056003
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2048, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056004
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2049, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056006
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2050, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056007
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2051, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056008
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 2052, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.ge2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.ge2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056009
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2053, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056010
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2054, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056011
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2055, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056012
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2056, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056013
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 2057, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.gi2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.gi2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056014
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 2058, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056015
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 2059, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056017
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2060, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2160.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056018
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2061, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2430.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2430.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2430, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056019
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2062, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2430.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2430.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2430, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2063, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2430.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2430.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2430, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2064, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2430.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2430.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2430, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056022
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2065, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2430.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2430.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2430, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056023
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2066, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2430.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2430.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2430, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056024
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2067, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2430.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2430.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2430, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056025
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2068, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2430.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2430.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2430, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056026
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2069, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2430.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2430.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2430, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056028
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2070, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2430.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2430.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2430, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 246056029
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2071, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2430.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2430.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2430, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056030
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2072, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2430.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2430.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2430, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056031
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2073, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2430.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2430.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2430, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056032
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2074, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2430.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2430.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2430, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056033
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2075, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2430.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2430.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2430, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056034
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2076, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2430.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2430.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2430, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056035
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2077, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2430.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2430.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2430, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056036
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 2078, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.2592.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': 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: 246056037
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 3, 'counter': 2079, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2592.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056039
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 2080, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2592.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056040
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 3, 'counter': 2081, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.2592.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': 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: 246056041
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 2082, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2592.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056042
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 2083, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2592.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056043
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 2084, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2592.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 246056044
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2085, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2592.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 246056045
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2086, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2592.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 246056046
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2087, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2592.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 246056047
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 2088, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2592.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': 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: 246056048
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2089, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2592.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': 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: 246056050
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 2090, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2592.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 246056051
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2091, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2592.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': 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: 246056052
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 2092, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2592.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': 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: 246056053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2160, 'characteristic': True, 'core_order': 27, 'counter': 2093, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '77760.bo.2880.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2880.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2880.du', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7330512212170881535, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 2880, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2\\times S_6', 'simple': False, 'solvable': True, 'special_labels': ['F', 'C4', 'F', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056054
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 2094, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2880.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2880.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056055
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 2095, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2880.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2880.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056056
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 2096, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2880.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2880.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056057
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 2097, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2880.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2880.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056058
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 2098, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2880.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2880.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056059
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 2099, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2880.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2880.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056062
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 3, 'counter': 2100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2880.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2880.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056063
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 2101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2880.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2880.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056064
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 2102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2880.i2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2880.i2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056065
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 2103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2880.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2880.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056066
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 2104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2880.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2880.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056067
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 2105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2880.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2880.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056068
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 2106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.2880.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2880.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 246056069
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056070
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.a2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056071
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056073
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056074
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056075
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.d2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.d2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056076
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056077
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056078
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056079
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.g2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.g2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056080
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246056081
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246056082
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056084
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056085
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056086
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056087
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056088
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056089
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056090
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056091
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056092
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056093
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056095
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.t2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.t2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056096
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056097
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 2132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.u2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.u2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056098
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056099
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 2134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.v2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.v2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056100
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056101
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.w2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.w2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056102
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056103
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.x2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.x2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056104
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056106
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 2140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.y2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.y2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056107
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056108
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056109
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056110
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056111
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056112
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056113
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056114
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056115
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056117
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056118
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056119
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056120
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056121
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056122
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 2155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056123
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 2156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056124
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056125
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 2158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.bp2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.bp2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056126
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056128
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056129
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056130
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 2162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.bs2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.bs2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056131
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056132
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056133
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056134
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 2166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.bv2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.bv2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056135
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056136
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246056137
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246056139
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056140
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056141
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056142
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056143
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056144
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056145
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056146
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cf2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.cf2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056147
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056148
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cg2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.cg2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056150
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056151
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ch2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ch2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056152
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056153
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ci2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ci2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056154
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056155
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056156
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056157
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056158
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056159
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056161
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056162
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056163
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056164
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056165
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cs2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.cs2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056166
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cs3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.cs3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056167
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cs4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.cs4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056168
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056169
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ct2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ct2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056170
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ct3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ct3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056173
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056174
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cu2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.cu2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056175
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056176
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056177
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cw2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.cw2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056178
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056179
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cx2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.cx2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056180
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056181
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056182
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056184
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.da2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.da2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056185
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056186
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056187
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.dc2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.dc2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056188
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056189
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.dd2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.dd2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056190
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056191
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056192
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056193
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056195
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056196
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056197
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056198
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056199
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 2224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246056200
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246056201
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056202
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 2227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246056203
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056204
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246056206
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056207
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246056208
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056209
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 2233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056210
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056211
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056212
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 2236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056213
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056214
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056215
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 2239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056217
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 2240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056218
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056219
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 2242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056220
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056221
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056222
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056223
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 2246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056224
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056225
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ej2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ej2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056226
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056228
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056229
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056230
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056231
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246056232
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246056233
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056234
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056235
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056236
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056237
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.et2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.et2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056239
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056240
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056241
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ev2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ev2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056242
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056243
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056244
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056245
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056246
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056247
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056248
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056250
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056251
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056252
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056253
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056254
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056255
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056256
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056257
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056258
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056259
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.fl2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.fl2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056261
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056262
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056265
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056266
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056267
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056268
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246056269
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 246056270
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056272
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056273
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056274
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056275
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056276
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056277
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056278
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056279
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056280
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056281
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056284
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056285
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056286
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056287
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056288
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056289
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056290
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056291
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056292
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056293
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 2309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056295
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056296
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056297
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056298
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056299
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056300
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056301
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056302
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056303
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056304
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056306
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ha1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056307
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.hb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056308
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.hc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056309
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.hd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056310
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.he1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056311
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.hf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056312
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.hg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056313
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.hh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056314
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.hi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': 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: 246056315
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.hj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056317
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.hk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056318
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.hl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056319
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.hm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056320
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.hn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056321
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ho1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056322
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.hp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056323
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.hq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056324
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.hr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056325
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.hs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.hs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056326
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ht1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ht1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056328
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.hu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.hu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056329
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.hv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.hv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056330
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 2342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.hw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.hw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056331
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.hx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.hx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056332
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.hy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.hy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056333
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.hz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.hz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056334
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ia1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ia1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056335
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ib1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.ib1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056336
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 2348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ic1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.ic1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056337
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.id1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.id1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056339
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.ie1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.ie1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056340
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 2351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3240.if1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.if1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 246056341
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3888.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': 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: 246056342
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3888.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': 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: 246056343
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 2354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3888.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 246056344
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3888.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': 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: 246056345
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3888.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': 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: 246056346
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3888.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246056347
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3888.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246056348
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.3888.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 246056350
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 720, 'characteristic': False, 'core_order': 18, 'counter': 2360, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '77760.bo.4320.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4320.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4320.bg', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8915526446794886175, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 4320, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times S_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 246056351
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4320.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056352
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4320.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056353
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4320.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056354
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2160, 'characteristic': False, 'core_order': 9, 'counter': 2364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056355
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 2365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056356
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 2366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056357
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056358
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 2368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4320.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056359
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4320.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056361
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4320.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056362
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2160, 'characteristic': False, 'core_order': 9, 'counter': 2371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056363
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2160, 'characteristic': False, 'core_order': 3, 'counter': 2372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056364
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056365
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056366
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056367
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056368
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 9, 'counter': 2377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4320.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056369
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 2378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4320.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056370
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 2379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4320.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056372
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 2380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4320.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056373
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 2381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4320.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056374
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4320.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056375
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4320.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056376
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4320.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056377
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4320.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056378
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 2386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056379
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056380
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056381
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 2389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056383
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056384
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056385
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 2392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056386
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 9, 'counter': 2393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4320.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056387
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 2394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4320.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056388
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 2395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056389
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056390
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056391
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056392
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4320.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056395
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 9, 'counter': 2400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056396
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 2401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056397
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056398
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056399
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056400
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056401
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056402
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056403
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056404
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056406
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056407
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 2411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056408
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 2412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056409
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 2413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056410
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056411
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056412
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 2416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4320.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056413
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 9, 'counter': 2417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056414
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 2418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056415
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 2419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056417
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056418
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 2421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056419
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056420
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056421
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056422
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056423
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056424
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056425
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056426
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056428
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056429
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056430
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056431
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056432
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 2434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056433
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056434
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056435
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 2437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056436
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056437
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 2439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056439
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056440
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056441
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056442
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056443
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056444
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056445
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 2446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056446
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056447
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 2448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056448
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 2449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056450
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 2450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056451
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056452
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056453
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056454
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 2454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056455
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4320.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 246056456
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056457
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056458
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056459
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056461
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 246056462
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.e2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.e2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 246056463
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056464
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056465
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 246056466
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056467
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056468
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056469
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056470
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056472
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056473
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 246056474
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056475
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056476
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 246056477
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.r2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.r2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 246056478
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056479
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056480
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 246056481
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 246056483
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.v2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.v2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 246056484
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056485
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056486
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056487
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056488
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056489
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056490
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 246056491
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056492
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056494
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 246056495
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056496
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056497
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056498
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 246056499
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056500
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056501
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056502
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.bm2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.bm2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056503
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056506
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056507
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056508
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056509
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056510
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056511
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056512
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056513
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056514
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056515
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056517
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056518
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056519
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056520
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056521
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056522
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056523
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056524
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056525
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056526
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056528
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.4860.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4860.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4860, 'quotient_simple': 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: 246056529
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 270, 'characteristic': False, 'core_order': 3, 'counter': 2521, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.5184.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': 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: 246056530
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 1, 'counter': 2522, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.5184.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': 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: 246056531
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 1, 'counter': 2523, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.5184.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': 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: 246056532
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 2524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056533
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056534
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056535
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056536
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056537
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056539
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056540
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056541
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056542
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056543
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056544
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056545
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056546
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056547
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 3, 'counter': 2538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056548
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056550
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 2540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056551
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056552
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056553
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 2543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056554
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056555
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 2545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056556
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1440, 'characteristic': False, 'core_order': 1, 'counter': 2546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056557
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1440, 'characteristic': False, 'core_order': 3, 'counter': 2547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056558
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 3, 'counter': 2548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056559
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056561
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056562
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056563
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 2552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056564
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056565
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056566
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 2555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056567
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056568
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056569
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 2558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056570
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056572
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056573
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 2561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056574
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 2562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056575
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056576
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056577
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056578
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056579
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056580
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.br2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.br2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056581
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056583
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 2570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.bs2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.bs2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056584
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056585
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.bt2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.bt2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056586
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056587
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056588
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056589
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056590
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 2577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.bx2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.bx2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056591
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056592
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.by2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.by2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056594
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056595
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.bz2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.bz2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056596
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056597
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056598
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056599
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 2585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056600
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 3, 'counter': 2586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.cd2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.cd2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056601
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 2587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056602
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 2588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.ce2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.ce2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056603
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056605
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 2590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.cf2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.cf2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056606
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056607
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056608
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 2593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056609
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056610
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.cj2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.cj2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056611
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056612
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 2597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.ck2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.ck2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056613
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056614
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.cl2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.cl2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056617
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056618
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 2601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.cm2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.cm2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056619
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056620
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.cn2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.cn2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056621
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056622
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.co2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.co2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056623
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056624
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056625
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056626
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056628
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056629
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056630
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 2612, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056631
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 2613, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056632
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2614, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056633
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056634
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056635
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 2617, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056636
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 2618, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056637
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 2619, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056639
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056640
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2621, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056641
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056642
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2623, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056643
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056644
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056645
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2626, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056646
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2627, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056647
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056648
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056650
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056651
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056652
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 2632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056653
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 2633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056654
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 246056655
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 2635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056656
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056657
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056658
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056659
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056661
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.dw2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.dw2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056662
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056663
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056664
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056665
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 2644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.dz2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.dz2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056666
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056667
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056668
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056669
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.ec2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.ec2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056670
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056672
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.ed2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.ed2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056673
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056674
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056675
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056676
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 2654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.eg2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.eg2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056677
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056678
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 2656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.6480.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6480.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 246056679
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 2657, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.7776.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': 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: 246056680
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 2658, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.7776.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': 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: 246056681
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.7776.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': 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: 246056683
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.7776.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': 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: 246056684
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.7776.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': 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: 246056685
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6480, 'characteristic': False, 'core_order': 9, 'counter': 2662, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '77760.bo.8640.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8640.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8640.t', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1113057395295209127, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 8640, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'D_6\\times S_6', 'simple': False, 'solvable': True, 'special_labels': ['C5', 'C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056686
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6480, 'characteristic': False, 'core_order': 3, 'counter': 2663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.8640.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8640.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8640, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056687
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': False, 'core_order': 3, 'counter': 2664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.8640.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8640.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8640, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056688
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 2665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.8640.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8640.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8640, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056689
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 2666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.8640.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8640.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8640, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056690
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 2667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.8640.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8640.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8640, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056691
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 2668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.8640.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8640.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8640, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056692
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 2669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.8640.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8640.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8640, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056694
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 2670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.8640.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8640.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8640, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056695
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 2671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.8640.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8640.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8640, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056696
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 2672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.8640.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8640.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8640, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056697
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 2673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.8640.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8640.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8640, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056698
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': False, 'core_order': 1, 'counter': 2674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.8640.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8640.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8640, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056699
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 2675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.8640.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8640.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8640, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056700
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 2676, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.8640.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8640.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8640, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 246056701
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2677, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056702
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2678, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.a2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056703
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2679, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056705
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 2680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.b2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056706
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056707
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.c2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.c2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056708
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056709
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056710
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056711
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056712
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056713
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056714
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 2689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056716
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056717
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056718
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.l2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.l2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056719
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056720
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 2694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.m2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.m2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056721
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056722
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.n2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.n2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056723
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056724
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056725
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056728
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056729
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056730
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056731
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056732
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.u2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.u2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056733
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.u3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.u3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056734
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056735
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.v2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.v2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056737
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056739
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2710, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.x2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.x2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2711, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056741
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056742
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056743
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 2714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056744
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056745
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056746
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056748
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 2719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056750
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056751
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.bh2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.bh2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056752
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2722, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056753
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2723, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056754
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056755
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056756
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056757
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056758
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056759
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056761
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2730, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056762
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056765
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2734, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056766
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2735, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056767
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2736, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056768
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2737, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056769
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056770
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2739, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056772
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2740, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056773
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2741, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056774
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2742, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056775
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2743, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056776
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056777
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056778
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056779
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2747, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056780
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2748, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056781
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.9720.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9720.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9720, 'quotient_simple': 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: 246056783
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4320, 'characteristic': False, 'core_order': 1, 'counter': 2750, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056784
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 2751, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056785
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2752, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056786
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4320, 'characteristic': False, 'core_order': 3, 'counter': 2753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12960.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056787
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1440, 'characteristic': False, 'core_order': 1, 'counter': 2754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12960.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056788
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4320, 'characteristic': False, 'core_order': 3, 'counter': 2755, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056789
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 2756, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056790
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2757, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056791
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4320, 'characteristic': False, 'core_order': 1, 'counter': 2758, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12960.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056792
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2160, 'characteristic': False, 'core_order': 1, 'counter': 2759, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12960.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056794
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2592, 'characteristic': False, 'core_order': 3, 'counter': 2760, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056795
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 2761, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056796
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 2762, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056797
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 1, 'counter': 2763, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056798
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 2764, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056799
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2765, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056800
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2766, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056801
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 1, 'counter': 2767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12960.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056802
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 3, 'counter': 2768, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056803
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 2769, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056805
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 2770, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056806
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 2771, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12960.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056807
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 2772, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056808
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2773, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056809
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2774, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056810
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 3, 'counter': 2775, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12960.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056811
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2776, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12960.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056812
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2777, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12960.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056813
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2778, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12960.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056814
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2779, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12960.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056816
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 3, 'counter': 2780, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056817
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2781, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056818
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2782, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056819
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 2783, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12960.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056820
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 2784, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12960.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056821
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2785, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12960.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056822
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2786, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12960.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056823
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2787, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12960.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056824
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2788, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056825
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 2789, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12960.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056827
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2790, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12960.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056828
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2791, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12960.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056829
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2792, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12960.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056830
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2793, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12960.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056831
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 2794, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056832
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2795, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12960.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056833
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2796, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12960.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056834
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2797, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12960.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056835
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2798, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12960.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056836
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2799, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.12960.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12960.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 246056839
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 540, 'characteristic': False, 'core_order': 1, 'counter': 2800, 'cyclic': True, 'direct': None, 'hall': 5, 'label': '77760.bo.15552.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '15552.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15552, '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': 5}
  • id: 246056840
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 1, 'counter': 2801, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056841
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 2802, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056842
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 2803, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056843
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2804, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056844
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 2880, 'characteristic': False, 'core_order': 1, 'counter': 2805, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056845
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 1, 'counter': 2806, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056846
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 2807, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056847
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 2808, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056848
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2809, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056850
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2810, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056851
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 2811, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.j2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.j2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056852
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2812, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056853
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 2813, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.k2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.k2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056854
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 2814, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056855
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': False, 'core_order': 1, 'counter': 2815, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.l2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.l2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056856
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2816, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056857
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 2817, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.m2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.m2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056858
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2818, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056859
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 2819, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.n2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.n2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056861
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2820, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056862
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2821, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056863
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 2822, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056864
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 2823, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056865
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2824, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056866
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2825, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056867
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2826, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056868
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2827, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056869
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 2828, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056870
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2829, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056872
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2830, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.x2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.x2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056873
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2831, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056874
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2832, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.y2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.y2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056875
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2833, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '77760.bo.19440.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19440.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 19440, 'quotient_simple': 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: 246056876
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 38880, 'characteristic': True, 'core_order': 3, 'counter': 2834, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '77760.bo.25920.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '25920.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '25920.w', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8300500786848619373, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 25920, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'S_3^2\\times S_6', 'simple': True, 'solvable': True, 'special_labels': ['Phi', 'C6', 'Phi', 'C6'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 246056877
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 12960, 'characteristic': False, 'core_order': 1, 'counter': 2835, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.25920.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '25920.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 25920, '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: 246056878
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 6480, 'characteristic': False, 'core_order': 1, 'counter': 2836, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.25920.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '25920.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 25920, '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: 246056879
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': False, 'core_order': 1, 'counter': 2837, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.25920.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '25920.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 25920, '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: 246056880
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': False, 'core_order': 1, 'counter': 2838, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.25920.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '25920.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 25920, '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: 246056881
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 2839, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.25920.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '25920.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 25920, '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: 246056883
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 2840, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.25920.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '25920.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 25920, '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: 246056884
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8640, 'characteristic': False, 'core_order': 1, 'counter': 2841, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.38880.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '38880.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 38880, '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: 246056885
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 8640, 'characteristic': False, 'core_order': 1, 'counter': 2842, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.38880.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '38880.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 38880, '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: 246056886
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 5184, 'characteristic': False, 'core_order': 1, 'counter': 2843, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.38880.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '38880.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 38880, '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: 246056887
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': False, 'core_order': 1, 'counter': 2844, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.38880.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '38880.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 38880, '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: 246056888
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 1, 'counter': 2845, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.38880.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '38880.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 38880, '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: 246056889
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 1, 'counter': 2846, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.38880.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '38880.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 38880, '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: 246056890
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 2847, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.38880.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '38880.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 38880, '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: 246056891
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 2848, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '77760.bo.38880.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '38880.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 38880, '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: 246056892
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '77760.bo', 'ambient_counter': 41, 'ambient_order': 77760, 'ambient_tex': 'C_3^2:D_6\\times S_6', 'central': True, 'central_factor': False, 'centralizer_order': 77760, 'characteristic': True, 'core_order': 1, 'counter': 2849, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '77760.bo.77760.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '77760.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '77760.bo', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4343203790838598385, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 77760, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2:D_6\\times S_6', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U0', 'C7', 'Z', 'U0', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 246056064
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2880.i2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['960.a1', '960.d1', '1440.df1'], 'contains': ['8640.d1', '8640.e1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 320, 'diagramx': None, 'generators': [280259527104, 193999420531, 80787], 'label': '77760.bo.2880.i2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '160.h1', 'old_label': '2880.i2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.i2', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 246054837
    {'ambient': '77760.bo', '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': '77760.a1', 'complements': ['77760.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1', '3.a1', '6.f1', '10.a1', '15.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [143975, 80787, 93924236159, 143304, 85805, 80880, 462320328386], 'label': '77760.bo.1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '77760.bo'}
  • id: 246054838
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': ['19440.d1', '19440.z1', '19440.e1', '19440.i1', '19440.x2', '19440.x1', '19440.c1', '19440.y1', '19440.h1', '19440.y2'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.d1'], 'contains': ['8.a1', '12.b1', '12.l1', '24.d1', '40.o1', '60.be1'], 'core': '4.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [462320323320, 143975, 93924409412, 80880, 80787], 'label': '77760.bo.4.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': ['2.a1', '2.d1'], 'normal_contains': ['8.a1', '12.b1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '77760.bo', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '25920.w'}
  • id: 246054839
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '18.a1', '18.d1', '18.l1'], 'contains': ['72.q1', '108.a1', '216.q1', '360.dx1', '540.gb1'], 'core': '108.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [462320368587, 143975, 93924374375], 'label': '77760.bo.36.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1', 'subgroup_fusion': None, 'weyl_group': '1440.5842'}
  • id: 246054840
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.ce2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.do1', '270.o1', '270.bc1', '270.br1'], 'contains': ['1080.di2', '1080.dq1', '1080.ec1', '1080.ez1', '1080.gc1', '1620.fn1', '1620.fo1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [462320225425, 448908007104, 19678982548, 461841188401, 80880, 80787], 'label': '77760.bo.540.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.ez1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ez1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246054841
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.do1', '270.h1', '270.be1', '270.br1'], 'contains': ['1080.dk2', '1080.dr1', '1080.ec1', '1080.fj1', '1080.gf1', '1620.fo1', '1620.fp1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [461841090505, 448908007104, 19678982548, 80880, 80787, 462320046985], 'label': '77760.bo.540.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '540.fa1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.fa1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246054842
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.dp1', '270.h1', '270.bc1', '270.bw1'], 'contains': ['1080.dm2', '1080.ds1', '1080.ec1', '1080.fu1', '1080.gg1', '1620.fq1', '1620.fr1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [462320323652, 19679028004, 143975, 461841148348, 80787, 448908278520], 'label': '77760.bo.540.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.fb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.fb1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246054843
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.dp1', '270.bx1'], 'contains': ['1080.dn2', '1080.dt1', '1080.ed1', '1080.fy1', '1080.gh1', '1620.fq1', '1620.fs1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [462320323891, 19679028004, 461841148348, 448908278667, 80787, 179159], 'label': '77760.bo.540.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '540.fc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.fc1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246054844
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.ce2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.dq1', '180.dr1', '180.ds1', '270.o1', '270.bd1', '270.bs1'], 'contains': ['1080.di1', '1080.dj1', '1080.dq1', '1080.dw1', '1080.ee1', '1080.gj1', '1080.hk1', '1620.ft1', '1620.fu1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841090505, 462320323320, 19679028004, 143975, 80787, 448908278520], 'label': '77760.bo.540.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.fd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.fd1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246054845
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.dq1', '270.c1', '270.i1', '270.bt1'], 'contains': ['1080.ej1', '1080.gk1', '1080.hl1', '1620.ft1', '1620.fw1', '2160.cv1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87661002480, 355462813680, 482768881, 462320006400, 80880, 375138086400], 'label': '77760.bo.540.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.fe1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.fe1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246054846
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.dq1', '270.bu1'], 'contains': ['1080.ek1', '1080.gl1', '1080.hm1', '1620.ft1', '1620.fx1', '2160.cw1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [461841004800, 462320288188, 448908283441, 19678982400, 224515, 262496684612], 'label': '77760.bo.540.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bu1', 'old_label': '540.ff1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ff1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246054847
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.ds1', '180.dt1', '270.j1', '270.be1', '270.bs1'], 'contains': ['1080.dk1', '1080.dl1', '1080.dr1', '1080.dx1', '1080.ee1', '1080.gq1', '1080.hn1', '1620.fu1', '1620.fv1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841004948, 462320052004, 448908001949, 19678982548, 80880, 80787], 'label': '77760.bo.540.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '540.fg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.fg1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246054848
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.dq1', '180.dt1', '270.k1', '270.p1', '270.bl1'], 'contains': ['1080.eg1', '1080.gr1', '1080.ho1', '1620.fu1', '1620.fw1', '1620.fx1', '2160.cy1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [19679028004, 462320052004, 448908001949, 461841050404, 262496586387, 80787], 'label': '77760.bo.540.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '540.fh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.fh1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246054849
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.dr1', '180.dt1', '270.l1'], 'contains': ['1080.eh1', '1080.gs1', '1080.hp1', '1620.fu1', '1620.fy1', '2160.cz1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [462320052004, 80787, 87661002387, 482635561, 355462813680, 375138086400], 'label': '77760.bo.540.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.k1', 'old_label': '540.fi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.fi1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
  • id: 246054850
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1', '18.m1'], 'contains': ['72.r1', '108.a1', '216.r1', '360.dy1', '540.gc1'], 'core': '108.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [462320368684, 93924409559, 179159], 'label': '77760.bo.36.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '36.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.r1', 'subgroup_fusion': None, 'weyl_group': '1440.5842'}
  • id: 246054851
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.dt1', '270.a1', '270.q1', '270.bt1'], 'contains': ['1080.ej1', '1080.gt1', '1080.hq1', '1620.fv1', '1620.fw1', '1620.fy1', '2160.da1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [355462732800, 462320368587, 482849425, 143975, 87660921600, 375138230375], 'label': '77760.bo.540.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.fj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.fj1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246054852
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.dt1', '270.bu1'], 'contains': ['1080.ek1', '1080.gu1', '1080.hr1', '1620.fv1', '1620.fx1', '1620.fy1', '2160.db1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [461841004800, 179012, 262496730115, 19678982400, 462320323320, 448908284158], 'label': '77760.bo.540.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bu1', 'old_label': '540.fk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.fk1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246054853
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.du1', '180.dv1', '180.dw1', '270.j1', '270.bd1', '270.bw1'], 'contains': ['1080.dm1', '1080.do1', '1080.ds1', '1080.dv1', '1080.ee1', '1080.gx1', '1080.hs1', '1620.fz1', '1620.ga1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [462320323320, 19679028004, 143975, 461841148348, 80787, 448908278520], 'label': '77760.bo.540.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.fl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.fl1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246054854
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.dw1', '180.dx1', '180.dy1', '270.bx1'], 'contains': ['1080.dn1', '1080.dp1', '1080.dt1', '1080.dz1', '1080.ef1', '1080.gy1', '1080.ht1', '1620.fz1', '1620.gb1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [462320323467, 19679028004, 461841148348, 448908278667, 80787, 179159], 'label': '77760.bo.540.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '540.fm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.fm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246054855
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.du1', '180.dx1', '270.k1', '270.bn1'], 'contains': ['1080.eg1', '1080.gz1', '1080.hu1', '1620.fz1', '1620.gc1', '2160.de1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [448908278999, 19679028004, 462320052004, 461841050404, 262496586387, 80787], 'label': '77760.bo.540.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '540.fn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.fn1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246054856
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.du1', '180.dv1', '180.dy1', '270.l1'], 'contains': ['1080.eh1', '1080.ha1', '1080.hv1', '1620.fz1', '1620.gd1', '2160.df1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [482808988, 355462876775, 462320052004, 87661002387, 80787, 375138086400], 'label': '77760.bo.540.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.l1', 'old_label': '540.fo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.fo1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246054857
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.dv1', '180.dx1', '180.dy1'], 'contains': ['1080.ei1', '1080.hb1', '1080.hw1', '1620.fz1', '1620.ge1', '2160.dg1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [448908278999, 262496649331, 19679028004, 462320052004, 461841050404, 80787], 'label': '77760.bo.540.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.fp1', 'old_label': '540.fp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.fp1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246054858
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.du1', '270.a1', '270.i1', '270.by1'], 'contains': ['1080.ej1', '1080.hi1', '1080.hx1', '1620.ga1', '1620.gc1', '1620.gd1', '2160.dh1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [355462732800, 482854584, 462320288188, 224515, 87660921600, 375138310915], 'label': '77760.bo.540.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '540.fq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.fq1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246054859
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.dx1', '270.bz1'], 'contains': ['1080.el1', '1080.hj1', '1080.hy1', '1620.gb1', '1620.gc1', '1620.ge1', '2160.di1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841004800, 262496649331, 462320287944, 19678982400, 143731, 448908243571], 'label': '77760.bo.540.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '540.fr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.fr1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246054860
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.dz1', '270.c1', '270.m1', '270.bv1'], 'contains': ['1080.eo1', '1080.gi1', '1080.hl1', '1620.fh1', '1620.gf1', '2160.dl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [355462732800, 462320283029, 87660926761, 482635561, 224515, 375138305994], 'label': '77760.bo.540.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.fs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.fs1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246054861
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.m1', '18.a1', '18.e1', '18.n1'], 'contains': ['72.q1', '108.r1', '216.s1', '360.fw1', '540.hj1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [45363, 93924230400, 462320328958], 'label': '77760.bo.36.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.s1', 'subgroup_fusion': None, 'weyl_group': '1440.5842'}
  • id: 246054862
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.dz1', '180.ea1', '270.n1', '270.p1', '270.bm1'], 'contains': ['1080.en1', '1080.gn1', '1080.ho1', '1620.fi1', '1620.gf1', '2160.dm1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [355462732800, 482849425, 462320225425, 87661059842, 375138270245, 80787], 'label': '77760.bo.540.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '540.ft1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ft1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246054863
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.ea1', '270.b1', '270.q1', '270.bv1'], 'contains': ['1080.eo1', '1080.gp1', '1080.hq1', '1620.fj1', '1620.gf1', '2160.dn1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [375138126985, 482635561, 355462813680, 87661007305, 80880, 462320046985], 'label': '77760.bo.540.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.fu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.fu1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246054864
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.eb1', '180.ec1', '270.n1', '270.bn1'], 'contains': ['1080.en1', '1080.gw1', '1080.hu1', '1620.fk1', '1620.gg1', '2160.dr1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [448908007204, 462320323891, 19679028004, 461841050404, 262496586387, 80787], 'label': '77760.bo.540.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '540.fv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.fv1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246054865
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.eb1', '270.b1', '270.m1', '270.by1'], 'contains': ['1080.eo1', '1080.he1', '1080.hx1', '1620.fl1', '1620.gg1', '2160.ds1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [482854584, 355462813680, 87661100280, 462320149704, 80880, 375138229704], 'label': '77760.bo.540.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '540.fw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.fw1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246054866
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.ec1', '270.bz1'], 'contains': ['1080.ep1', '1080.hg1', '1080.hy1', '1620.fm1', '1620.gg1', '2160.dt1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841004800, 262496684759, 19678982400, 448908323884, 462320369015, 179159], 'label': '77760.bo.540.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '540.fx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.fx1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246054867
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.dj2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.ed1', '180.ee1', '270.o1', '270.be1', '270.bw1'], 'contains': ['1080.du1', '1080.ea1', '1080.ec1', '1080.ee1', '1080.hz1', '1620.gh1', '1620.gi1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [462320323320, 19679028004, 143975, 461841050404, 80787, 448908278520], 'label': '77760.bo.540.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '540.fy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.fy1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246054868
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.dk2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.ed1', '180.ef1', '270.bx1'], 'contains': ['1080.dy1', '1080.eb1', '1080.ed1', '1080.ef1', '1080.ia1', '1620.gh1', '1620.gj1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [462320323467, 19679028004, 461841050404, 448908278667, 80787, 179159], 'label': '77760.bo.540.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bi1', 'old_label': '540.fz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.fz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246054869
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.cj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.a1', '180.ee1', '180.ef1', '270.p1', '270.bn1'], 'contains': ['1080.eg1', '1080.en1', '1080.if1', '1620.gh1', '1620.gk1', '2160.dx1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [448908007204, 19679028004, 462320052004, 461841050404, 262496586387, 80787], 'label': '77760.bo.540.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '540.ga1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ga1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246054870
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.q1', '180.ee1', '270.c1', '270.q1', '270.by1'], 'contains': ['1080.ej1', '1080.eo1', '1080.ig1', '1620.gi1', '1620.gk1', '2160.dy1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [355462732800, 462320368587, 482630400, 143975, 87660921600, 375138230375], 'label': '77760.bo.540.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '540.gb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.gb1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246054871
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.r1', '180.ef1', '270.bz1'], 'contains': ['1080.el1', '1080.ep1', '1080.ih1', '1620.gj1', '1620.gk1', '2160.dz1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841004800, 462320368684, 262496684759, 19678982400, 448908323884, 179159], 'label': '77760.bo.540.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '540.gc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.gc1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246054872
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.c1', '12.m1', '18.c1', '18.f1', '18.k1'], 'contains': ['72.a1', '108.r1', '216.t1', '360.ga1', '540.hk1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [93924311187, 462320328958, 80787], 'label': '77760.bo.36.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.t1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
  • id: 246054873
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.eg1', '270.f1', '270.bf1', '270.br1'], 'contains': ['1080.et1', '1080.ez1', '1080.fq1', '1080.fz1', '1080.gf1', '1620.gl1', '1620.gn1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [448908278999, 461841090505, 19678982548, 462320328958, 80880, 80787], 'label': '77760.bo.540.gd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.gd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.gd1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246054874
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.ej1', '270.h1', '270.bf1', '270.bp1'], 'contains': ['1080.et2', '1080.ew1', '1080.fc1', '1080.fu1', '1080.gf1', '1620.gm1', '1620.gv1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [461841223825, 462320323799, 448908283441, 19679028004, 143975, 80787], 'label': '77760.bo.540.ge1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.ge1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ge1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246054875
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.eg1', '270.r1', '270.ba1', '270.br1'], 'contains': ['1080.fd1', '1080.fj1', '1080.fp1', '1080.fz1', '1080.gc1', '1620.gn1', '1620.go1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [448908278999, 461841009961, 19679028004, 143975, 462320328958, 80787], 'label': '77760.bo.540.gf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.gf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.gf1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246054876
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.eh1', '270.g1', '270.ba1', '270.bq1'], 'contains': ['1080.eu1', '1080.ev1', '1080.fd1', '1080.fi1', '1080.fm2', '1080.fr1', '1080.gb1', '1620.gp1', '1620.gt1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841009961, 448908283441, 19679028004, 143975, 462320328958, 80787], 'label': '77760.bo.540.gg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.gg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.gg1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246054877
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.eh1', '270.f1', '270.bb1', '270.bq1'], 'contains': ['1080.et1', '1080.ey1', '1080.fe1', '1080.fg1', '1080.fm1', '1080.fr1', '1080.gd1', '1620.gq1', '1620.gt1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841090505, 448908001949, 19678982548, 462320328958, 80880, 80787], 'label': '77760.bo.540.gh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.gh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.gh1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246054878
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.ei1', '270.g1', '270.bb1', '270.bp1'], 'contains': ['1080.et2', '1080.ev1', '1080.fd2', '1080.fg1', '1080.fn1', '1080.ft1', '1080.ge1', '1620.gr1', '1620.gu1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841223825, 462320323891, 19679028004, 143975, 448908284158, 80787], 'label': '77760.bo.540.gi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.gi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.gi1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246054879
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.ek1', '270.h1', '270.ba1', '270.ca1'], 'contains': ['1080.ex1', '1080.fc1', '1080.fj1', '1080.fm2', '1080.gg1', '1620.gs1', '1620.gy1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [448908283441, 19679028004, 143975, 462320328958, 461841183388, 80787], 'label': '77760.bo.540.gj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.gj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.gj1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246054880
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.ej1', '270.r1', '270.bc1', '270.bp1'], 'contains': ['1080.fd2', '1080.ff1', '1080.fo1', '1080.fu1', '1080.gc1', '1620.gv1', '1620.gw1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [462320230444, 448908001949, 19678982548, 461841188401, 80880, 80787], 'label': '77760.bo.540.gk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.gk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.gk1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246054881
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.ek1', '270.f1', '270.bc1', '270.ca1'], 'contains': ['1080.ez1', '1080.fh1', '1080.fm1', '1080.fo1', '1080.gg1', '1620.gx1', '1620.gy1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [462320225425, 448908001949, 461841148348, 19678982548, 80880, 80787], 'label': '77760.bo.540.gl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.gl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.gl1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246054882
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.el1', '270.a1', '270.s1', '270.bv1'], 'contains': ['1080.gi1', '1080.hi1', '1080.hq1', '1620.ha1', '1620.hb1', '1620.hc1', '2160.fp1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87661244013, 462320283450, 355462778163, 375138363450, 482635561, 45363], 'label': '77760.bo.540.gm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.gm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.gm1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246054883
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.c1', '18.b1', '18.d1', '18.n1'], 'contains': ['72.q1', '108.r1', '216.u1', '360.gc1', '540.hl1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93924230400, 80880, 462320046985], 'label': '77760.bo.36.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.u1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.u1', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
  • id: 246054884
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.em1', '180.en1', '270.g1', '270.bf1', '270.bs1'], 'contains': ['1080.et2', '1080.eu1', '1080.fq1', '1080.fw1', '1080.gj1', '1080.hc1', '1080.hn1', '1620.gz1', '1620.hd1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841223825, 448908278999, 462320323799, 19679028004, 143975, 80787], 'label': '77760.bo.540.gn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.gn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.gn1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246054885
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.em1', '270.b1', '270.s1', '270.bt1'], 'contains': ['1080.gk1', '1080.he1', '1080.hq1', '1620.gz1', '1620.he1', '2160.ft1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841004800, 462320288371, 448908283441, 262496730115, 19678982400, 224515], 'label': '77760.bo.540.go1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.go1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.go1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246054886
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.em1', '270.bu1'], 'contains': ['1080.gl1', '1080.hf1', '1080.hr1', '1620.gz1', '1620.hf1', '2160.fu1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [87661238852, 375138449015, 482635561, 355462813680, 45363, 462320369015], 'label': '77760.bo.540.gp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bu1', 'old_label': '540.gp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.gp1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246054887
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.el1', '180.eq1', '270.j1', '270.bf1', '270.bq1'], 'contains': ['1080.et1', '1080.eu1', '1080.ew1', '1080.fb1', '1080.gm1', '1080.gx1', '1080.hn1', '1620.ha1', '1620.hk1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841090505, 19678982548, 462320328958, 80880, 80787, 448908283914], 'label': '77760.bo.540.gq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.gq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.gq1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246054888
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.el1', '180.eo1', '270.k1', '270.t1', '270.bm1'], 'contains': ['1080.gn1', '1080.gz1', '1080.ho1', '1620.hb1', '1620.hk1', '2160.fr1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87661279197, 355462732800, 482635561, 375138363450, 462320328958, 80787], 'label': '77760.bo.540.gr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '540.gr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.gr1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246054889
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.gs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.el1', '180.ep1', '270.l1'], 'contains': ['1080.go1', '1080.ha1', '1080.hp1', '1620.hc1', '1620.hk1', '2160.fs1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [448908278999, 19679028004, 461841050404, 262496684612, 80787, 462320046749], 'label': '77760.bo.540.gs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.l1', 'old_label': '540.gs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.gs1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246054890
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.gt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.eo1', '270.d1', '270.i1', '270.bv1'], 'contains': ['1080.gp1', '1080.hi1', '1080.hl1', '1620.hb1', '1620.hl1', '2160.fz1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [355462732800, 87661140625, 482635561, 375138092159, 224515, 462320283450], 'label': '77760.bo.540.gt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.gt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.gt1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246054891
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.gu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.em1', '180.er1', '270.n1', '270.t1', '270.bl1'], 'contains': ['1080.gr1', '1080.gw1', '1080.ho1', '1620.hd1', '1620.he1', '1620.hf1', '2160.gd1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [462320323799, 19679028004, 448908001949, 461841050404, 262496586387, 80787], 'label': '77760.bo.540.gu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '540.gu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.gu1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246054892
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.gv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.en1', '180.er1', '270.r1', '270.bb1', '270.bs1'], 'contains': ['1080.fd2', '1080.fe1', '1080.fp1', '1080.fv1', '1080.gq1', '1080.hc1', '1080.hk1', '1620.hd1', '1620.hg1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [448908278999, 462320323891, 19678982548, 461841281758, 80880, 80787], 'label': '77760.bo.540.gv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.gv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.gv1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246054893
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.gw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.er1', '270.d1', '270.m1', '270.bt1'], 'contains': ['1080.gt1', '1080.he1', '1080.hl1', '1620.he1', '1620.hg1', '2160.gf1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841004800, 262496649575, 19678982400, 143975, 448908284158, 462320369015], 'label': '77760.bo.540.gw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.gw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.gw1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246054894
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1', '12.o1', '18.f1', '18.j1'], 'contains': ['72.a1', '108.s1', '216.v1', '360.gd1', '540.hm1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93924311187, 462320323891, 80787], 'label': '77760.bo.36.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.v1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.v1', 'subgroup_fusion': None, 'weyl_group': '1440.5842'}
  • id: 246054895
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.gx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.er1', '270.bu1'], 'contains': ['1080.gu1', '1080.hf1', '1080.hm1', '1620.hf1', '1620.hg1', '2160.gg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [355462778163, 87661100280, 482768881, 462320149704, 80880, 375138229704], 'label': '77760.bo.540.gx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bu1', 'old_label': '540.gx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.gx1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246054896
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.gy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.es1', '270.b1', '270.i1', '270.cb1'], 'contains': ['1080.gk1', '1080.gp1', '1080.hx1', '1620.hi1', '1620.hm1', '2160.ga1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841004800, 448908283441, 262496730115, 19678982400, 224515, 462320328958], 'label': '77760.bo.540.gy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.gy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.gy1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246054897
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.gz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.ev1', '270.a1', '270.m1', '270.cb1'], 'contains': ['1080.gi1', '1080.gt1', '1080.hx1', '1620.hh1', '1620.hi1', '1620.hj1', '2160.gh1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87661105201, 482854584, 462320225425, 355462813680, 375138305425, 80880], 'label': '77760.bo.540.gz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.gz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.gz1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246054898
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ha1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.eu1', '180.ev1', '270.j1', '270.bb1', '270.ca1'], 'contains': ['1080.ex1', '1080.fa1', '1080.fm1', '1080.fn1', '1080.gm1', '1080.gq1', '1080.hs1', '1620.hh1', '1620.hn1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841367555, 19678982548, 462320328958, 80880, 80787, 448908283914], 'label': '77760.bo.540.ha1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.ha1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ha1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246054899
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.hb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.es1', '180.ev1', '270.k1', '270.n1', '270.bo1'], 'contains': ['1080.gn1', '1080.gr1', '1080.hu1', '1620.hi1', '1620.hn1', '2160.gj1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [482808988, 355462732800, 462320225425, 87661059842, 375138270245, 80787], 'label': '77760.bo.540.hb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '540.hb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.hb1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246054900
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.hc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.et1', '180.ev1', '270.l1'], 'contains': ['1080.go1', '1080.gs1', '1080.hv1', '1620.hj1', '1620.hn1', '2160.gk1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [482808988, 462320225425, 87661059842, 355462813680, 375138270245, 80787], 'label': '77760.bo.540.hc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.l1', 'old_label': '540.hc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.hc1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246054901
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.hd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.eo1', '180.ep1', '180.eq1', '270.r1', '270.bd1', '270.bq1'], 'contains': ['1080.fd1', '1080.fe1', '1080.ff1', '1080.fl1', '1080.gv1', '1080.gx1', '1080.hk1', '1620.hk1', '1620.hl1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841090505, 19679028004, 143975, 448908284158, 462320328958, 80787], 'label': '77760.bo.540.hd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.hd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.hd1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246054902
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.he1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.es1', '180.et1', '180.eu1', '270.g1', '270.bd1', '270.ca1'], 'contains': ['1080.fh1', '1080.fk1', '1080.fm2', '1080.fn1', '1080.gj1', '1080.gv1', '1080.hs1', '1620.hm1', '1620.hn1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [19679028004, 143975, 461841148348, 448908284158, 462320328958, 80787], 'label': '77760.bo.540.he1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.he1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.he1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246054903
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.hf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.ce2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.ew1', '180.ey1', '270.o1', '270.bf1', '270.ca1'], 'contains': ['1080.ez1', '1080.fc1', '1080.gj1', '1080.gm1', '1080.hz1', '1620.ho1', '1620.hp1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [448908283441, 19679028004, 143975, 461841050404, 80787, 462320328241], 'label': '77760.bo.540.hf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.hf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.hf1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246054904
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.hg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.ew1', '180.ez1', '270.r1', '270.be1', '270.ca1'], 'contains': ['1080.fj1', '1080.fo1', '1080.gq1', '1080.gv1', '1080.hz1', '1620.hp1', '1620.hq1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [19679028004, 143975, 448908284158, 461841050404, 462320328958, 80787], 'label': '77760.bo.540.hg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '540.hg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.hg1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246054905
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.n1', '18.b1', '18.e1', '18.l1'], 'contains': ['72.q1', '108.s1', '216.w1', '360.ge1', '540.hn1'], 'core': '216.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [143975, 93924374375, 462320369015], 'label': '77760.bo.36.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.w1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.w1', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
  • id: 246054906
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.hh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.ex1', '180.fa1', '270.r1', '270.bf1', '270.bw1'], 'contains': ['1080.fu1', '1080.fz1', '1080.gx1', '1080.hc1', '1080.hz1', '1620.hr1', '1620.hs1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [448908278999, 461841004948, 462320323891, 19678982548, 80880, 80787], 'label': '77760.bo.540.hh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.hh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.hh1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246054907
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.hi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.ex1', '180.fb1', '270.bx1'], 'contains': ['1080.fy1', '1080.ga1', '1080.gy1', '1080.hd1', '1080.ia1', '1620.hr1', '1620.ht1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [448908278999, 462320323799, 19679028004, 461841050404, 80787, 179159], 'label': '77760.bo.540.hi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '540.hi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.hi1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246054908
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.hj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.s1', '180.ey1', '270.c1', '270.s1', '270.cb1'], 'contains': ['1080.gi1', '1080.gk1', '1080.ig1', '1620.ho1', '1620.hu1', '2160.ev1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [375138408958, 355462778163, 482711044, 87661279434, 45363, 462320328958], 'label': '77760.bo.540.hj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.hj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.hj1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246054909
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.hk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.t1', '180.ey1', '180.ez1', '270.p1', '270.t1', '270.bo1'], 'contains': ['1080.gn1', '1080.gr1', '1080.if1', '1620.hp1', '1620.hu1', '2160.ew1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [87661279197, 355462732800, 482676004, 375138363450, 462320328958, 80787], 'label': '77760.bo.540.hk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '540.hk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.hk1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246054910
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.hl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.u1', '180.ez1', '270.d1', '270.q1', '270.cb1'], 'contains': ['1080.gp1', '1080.gt1', '1080.ig1', '1620.hq1', '1620.hu1', '2160.ex1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [355462732800, 87661140625, 375138127292, 482630400, 143975, 462320328958], 'label': '77760.bo.540.hl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.hl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.hl1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246054911
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.hm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.v1', '180.fa1', '180.fb1', '270.t1', '270.bn1'], 'contains': ['1080.gw1', '1080.gz1', '1080.if1', '1620.hr1', '1620.hv1', '2160.ey1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [448908278999, 462320323799, 19679028004, 461841050404, 262496586387, 80787], 'label': '77760.bo.540.hm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '540.hm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.hm1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246054912
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.hn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.w1', '180.fa1', '270.d1', '270.s1', '270.by1'], 'contains': ['1080.he1', '1080.hi1', '1080.ig1', '1620.hs1', '1620.hv1', '2160.ez1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [355462778163, 87661238852, 482711044, 375138449015, 45363, 462320369015], 'label': '77760.bo.540.hn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '540.hn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.hn1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246054913
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ho1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.x1', '180.fb1', '270.bz1'], 'contains': ['1080.hg1', '1080.hj1', '1080.ih1', '1620.ht1', '1620.hv1', '2160.fa1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [355462732800, 482630400, 87661100280, 375138086998, 462320369015, 179159], 'label': '77760.bo.540.ho1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '540.ho1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ho1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246054914
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '576.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.a1', '288.b1', '288.c1', '288.d1', '288.e1'], 'contains': ['1728.a1', '1728.b1', '2880.a1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [143975, 18764570163, 80880, 80787], 'label': '77760.bo.576.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '576.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.a1', 'subgroup_fusion': None, 'weyl_group': '144.143'}
  • id: 246054915
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '648.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.b1', '216.c1', '324.d1'], 'contains': ['1296.a1', '1296.q1', '1296.r1', '1944.a1', '3240.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [86155, 269202614155, 148, 181146153355, 267841814255], 'label': '77760.bo.648.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d1', 'old_label': '648.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 246054916
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1', '18.m1'], 'contains': ['72.r1', '108.s1', '216.x1', '360.gf1', '540.ho1'], 'core': '216.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [93924409559, 462320369015, 179159], 'label': '77760.bo.36.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '36.x1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.x1', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
  • id: 246054917
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '648.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.c1', '216.d1', '324.d1'], 'contains': ['1296.a1', '1296.s1', '1296.t1', '1944.b1', '3240.k1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [269202712074, 267842004721, 143975, 85805, 181146153355], 'label': '77760.bo.648.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d1', 'old_label': '648.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.b1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246054918
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '648.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.w1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.d1', '216.b1', '216.e1', '216.f1', '324.a1', '324.b1', '324.c1'], 'contains': ['1296.w1', '3240.o1', '3888.a1', '6480.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [183845, 455574067200, 349232267045], 'label': '77760.bo.648.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '648.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.c1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
  • id: 246054919
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '648.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.e1', '216.c1', '216.g1', '324.e1'], 'contains': ['1296.c1', '1296.n1', '1296.o1', '1944.a1', '3240.z1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [181146153005, 269202533066, 267841768585, 85805, 80787], 'label': '77760.bo.648.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '648.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.d1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246054920
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '648.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.h1', '216.d1', '216.h1', '324.e1'], 'contains': ['1296.c1', '1296.o1', '1296.p1', '1944.b1', '3240.bc1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [181146153005, 86155, 267841768892, 269202533759, 80787], 'label': '77760.bo.648.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.e1', 'old_label': '648.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.e1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246054921
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '648.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.f1', '216.g1', '324.d1'], 'contains': ['1296.d1', '1296.q1', '1296.s1', '1944.a1', '3240.bd1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [183845, 269202614155, 267842005050, 143975, 181146153355], 'label': '77760.bo.648.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d1', 'old_label': '648.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.f1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246054922
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '648.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.g1', '216.h1', '324.d1'], 'contains': ['1296.d1', '1296.r1', '1296.t1', '1944.b1', '3240.bg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [183845, 269202614155, 267842005050, 143975, 181146251274], 'label': '77760.bo.648.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d1', 'old_label': '648.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.g1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246054923
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '648.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.i1', '216.i1', '324.d1'], 'contains': ['1296.a1', '1296.b1', '1296.d1', '1296.e1', '1296.g1', '1296.k1', '1296.m1', '1944.c1', '3240.bm1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1037980104, 143975, 5066, 18764663042, 143304], 'label': '77760.bo.648.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d1', 'old_label': '648.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.h1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246054924
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '648.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.j1', '216.i1', '324.e1'], 'contains': ['1296.c1', '1296.f1', '1296.h1', '1296.i1', '1296.j1', '1944.c1', '3240.bo1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1037980104, 85805, 80787, 18764663042, 143304], 'label': '77760.bo.648.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.e1', 'old_label': '648.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.i1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246054925
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '648.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.l1', '216.k1', '216.m1', '324.e1'], 'contains': ['1296.i1', '1296.n1', '1296.p1', '1944.d1', '3240.bx1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [267841773954, 181146067893, 269202609094, 80787, 693], 'label': '77760.bo.648.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.e1', 'old_label': '648.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.j1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 246054926
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '648.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.m1', '216.l1', '324.e1'], 'contains': ['1296.i1', '1296.o1', '1944.e1', '3240.ca1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [267841773954, 269202609094, 80787, 181146153355, 693], 'label': '77760.bo.648.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.e1', 'old_label': '648.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.k1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246055024
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.bi1', '360.b1', '360.g1', '360.cc1'], 'contains': ['1440.bb1', '1440.bm1', '1440.cr1', '2160.cv1', '2160.dl1', '2160.dq1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [456053074316, 93448857748, 148, 180587237516, 174400128148], 'label': '77760.bo.720.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '720.cz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.cz1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246054927
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '40.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['20.d1'], 'contains': ['80.a1', '80.c1', '80.d1', '80.j1', '80.k1', '80.r1', '80.s1', '120.a1', '120.f1', '120.g1', '120.h1', '120.i1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 80, 'diagramx': None, 'generators': [180587456184, 93449001331, 143975, 83641651, 174400173363, 85805, 80880, 80787], 'label': '77760.bo.40.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '40.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.a1', 'subgroup_fusion': None, 'weyl_group': '3888.ik'}
  • id: 246054928
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '648.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.n1', '216.j1', '216.n1', '216.o1', '324.c1', '324.f1', '324.g1'], 'contains': ['1296.w1', '3240.cd1', '3888.d1', '6480.bd1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [25470547200, 286482873600, 143304], 'label': '77760.bo.648.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '648.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.l1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
  • id: 246054929
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '648.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.o1', '216.k1', '324.d1'], 'contains': ['1296.k1', '1296.q1', '1296.t1', '1944.d1', '3240.ck1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [181146067893, 143975, 269202528693, 267842090615, 143304], 'label': '77760.bo.648.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '648.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.m1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246054930
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '648.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.q1', '216.l1', '324.d1'], 'contains': ['1296.k1', '1296.r1', '1296.s1', '1944.e1', '3240.cn1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [143975, 143304, 181146153355, 269202528693, 267842090615], 'label': '77760.bo.648.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d1', 'old_label': '648.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.n1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246054931
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '648.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.p1', '216.m1'], 'contains': ['1296.l1', '1296.u1', '1296.v1', '1944.d1', '3240.co1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [181146067893, 267842045252, 224184, 269202528693, 224612], 'label': '77760.bo.648.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.m1', 'old_label': '648.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.o1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246054932
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '648.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.a1', '216.p1', '216.q1', '216.r1', '324.a1', '324.f1'], 'contains': ['1296.w1', '3240.ei1', '3888.f1', '6480.ci1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [443555481600, 479001600], 'label': '77760.bo.648.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '648.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.p1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
  • id: 246054933
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '648.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.w1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.r1', '216.s1', '216.t1', '216.u1', '324.a1', '324.b1', '324.g1'], 'contains': ['1296.w1', '3240.ha1', '3888.g1', '6480.dn1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [174879170185, 462320046985], 'label': '77760.bo.648.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '648.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.q1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
  • id: 246054934
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '648.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.s1', '216.v1', '216.w1', '216.x1', '324.b1', '324.f1'], 'contains': ['1296.w1', '3240.hl1', '3888.h1', '6480.do1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [174879492215, 462320369015], 'label': '77760.bo.648.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '648.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.r1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
  • id: 246054935
    {'ambient': '77760.bo', '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': '108.a1', 'complements': ['108.a1', '108.r1', '108.s1'], 'conjugacy_class_count': 1, 'contained_in': ['144.c1', '240.s1', '360.bs1', '360.bt1'], 'contains': ['1440.a1', '1440.b1', '2160.bn1'], 'core': '720.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [143975, 85805, 80880, 80787, 143304], 'label': '77760.bo.720.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '720.a1', 'normal_contained_in': ['2.c1'], 'normal_contains': ['1440.a1', '1440.b1'], 'normalizer': '1.a1', 'old_label': '720.a1', 'projective_image': '77760.bo', 'quotient_action_image': '1.1', 'quotient_action_kernel': '720.763', 'quotient_action_kernel_order': 720, 'quotient_fusion': None, 'short_label': '720.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246054936
    {'ambient': '77760.bo', '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': '4320.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.a1', '360.a1', '360.b1', '360.v1'], 'contains': ['1440.c1', '1440.bb1', '1440.bm1', '2160.a1', '2160.b1', '2160.c1', '2160.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [93449082115, 456053207518, 174400128000, 224515, 85946], 'label': '77760.bo.720.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '720.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246054937
    {'ambient': '77760.bo', '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': '12960.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.b1', '360.b1', '360.c1', '360.d1', '360.e1', '360.w1'], 'contains': ['1440.c1', '1440.bi1', '1440.cr1', '2160.e1', '2160.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [193999501315, 5161, 280259486761, 482635561, 224515], 'label': '77760.bo.720.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '720.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.c1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246054938
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '40.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['20.a1', '20.b1', '20.d1'], 'contains': ['80.a1', '80.b1', '80.j1', '80.l1', '80.m1', '120.b1', '120.j1', '120.k1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [143975, 80787, 83641651, 174400173363, 180587277504, 93449001331, 183845, 80880], 'label': '77760.bo.40.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.b1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246054939
    {'ambient': '77760.bo', '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': '12960.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.c1', '360.a1', '360.c1', '360.v1'], 'contains': ['1440.c1', '1440.bx1', '1440.ck1', '2160.g1', '2160.h1', '2160.i1', '2160.j1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [456053154955, 174400128000, 143975, 85805, 93449001575], 'label': '77760.bo.720.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '720.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.d1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246054940
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.d1', '360.a1', '360.w1'], 'contains': ['1440.c1', '1440.cw1', '1440.dg1', '2160.k1', '2160.l1', '2160.m1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [193999501315, 5161, 482849425, 280259486761, 224515], 'label': '77760.bo.720.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '720.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.e1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246054941
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.w1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.d1', '240.a1', '240.e1', '360.f1', '360.k1', '360.bp1'], 'contains': ['1440.d1', '1440.q1', '1440.bk1', '2160.a1', '2160.o1', '2160.p1', '2160.q1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [40349, 143975, 375138225118, 174436501946, 80787], 'label': '77760.bo.720.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '720.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.f1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246054942
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.bb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.e1', '240.a1', '240.h1', '360.h1', '360.k1', '360.bq1'], 'contains': ['1440.d1', '1440.v1', '1440.bn1', '2160.b1', '2160.o1', '2160.s1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [183845, 442641024148, 442162067904, 80880, 80787], 'label': '77760.bo.720.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '720.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.g1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246054943
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.a1', '240.f1', '360.i1'], 'contains': ['1440.e1', '1440.x1', '1440.bt1', '2160.c1', '2160.q1', '2160.s1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [40349, 174400208787, 93449036612, 456053073961, 80787], 'label': '77760.bo.720.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1', 'old_label': '720.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.h1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246054944
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.n1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.a1', '240.g1', '360.j1', '360.l1', '360.x1'], 'contains': ['1440.f1', '1440.z1', '1440.bu1', '2160.d1', '2160.p1', '2160.s1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [174400208787, 93448938387, 85805, 83462400, 80787], 'label': '77760.bo.720.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '720.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.i1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246054945
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.g1', '360.g1', '360.m1', '360.v1'], 'contains': ['1440.g1', '1440.bb1', '1440.bx1', '2160.d1', '2160.r1', '2160.t1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [174400208880, 40585, 456053073961, 93448938480, 80880], 'label': '77760.bo.720.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '720.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.j1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246054946
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.b1', '180.o1', '240.b1', '240.i1', '360.k1', '360.n1', '360.br1'], 'contains': ['1440.d1', '1440.bf1', '1440.cn1', '2160.e1', '2160.u1', '2160.v1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [86155, 88176216811, 80880, 80787, 113567005680], 'label': '77760.bo.720.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '720.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.k1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246054947
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.b1', '240.j1', '360.l1', '360.q1', '360.r1', '360.s1', '360.y1'], 'contains': ['1440.f1', '1440.bh1', '1440.cu1', '2160.f1', '2160.v1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [40349, 280259521949, 482635561, 80787, 193999357587], 'label': '77760.bo.720.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '720.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.l1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246054948
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.j1', '360.m1', '360.p1', '360.t1', '360.u1', '360.w1'], 'contains': ['1440.g1', '1440.bi1', '1440.cw1', '2160.f1', '2160.w1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [280259486761, 482635561, 193999276800, 40585, 80880], 'label': '77760.bo.720.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '720.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.m1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246054949
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': ['19440.j1', '19440.j2', '19440.a1', '19440.i1', '19440.z1', '19440.d1', '19440.e1', '19440.x2', '19440.x1', '19440.c1', '19440.k1', '19440.f1', '19440.k2'], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.b1', '2.e1'], 'contains': ['8.a1', '12.c1', '12.m1', '24.e1', '40.q1', '60.bi1'], 'core': '4.d1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [143975, 93924409412, 80880, 80787, 462320328386], 'label': '77760.bo.4.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': ['2.a1', '2.b1', '2.e1'], 'normal_contains': ['8.a1', '12.c1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '77760.bo', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': '77760.bo'}
  • id: 246054950
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '40.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['20.a1', '20.c1', '20.d1'], 'contains': ['80.b1', '80.c1', '80.m1', '80.n1', '80.r1', '120.c1', '120.l1', '120.n1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [180587277504, 183845, 456053207518, 93449001331, 143975, 174400173363, 80880, 80787], 'label': '77760.bo.40.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.c1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246054951
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.l1', '360.g1', '360.p1', '360.v1'], 'contains': ['1440.g1', '1440.bm1', '1440.ck1', '2160.i1', '2160.x1', '2160.z1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [93449082115, 456053207518, 138242, 174400128000, 224515], 'label': '77760.bo.720.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '720.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.n1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246054952
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.n1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.j1', '240.c1', '240.m1', '360.h1', '360.n1', '360.bp1'], 'contains': ['1440.d1', '1440.bo1', '1440.bz1', '2160.g1', '2160.y1', '2160.ba1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [40349, 143975, 174436501946, 375138172555, 80787], 'label': '77760.bo.720.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '720.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.o1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246054953
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.c1', '240.k1', '360.i1'], 'contains': ['1440.e1', '1440.bs1', '1440.cb1', '2160.h1', '2160.y1', '2160.bc1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [93448938387, 456053154955, 174400307012, 85805, 80787], 'label': '77760.bo.720.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.i1', 'old_label': '720.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.p1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246054954
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.c1', '240.l1', '360.j1', '360.q1', '360.x1'], 'contains': ['1440.f1', '1440.bu1', '1440.cd1', '2160.i1', '2160.y1', '2160.bb1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [40349, 174400208787, 83543730, 93448938387, 80787], 'label': '77760.bo.720.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.r1', 'old_label': '720.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.q1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246054955
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.k1', '240.c1', '240.n1', '360.f1', '360.n1', '360.bq1'], 'contains': ['1440.d1', '1440.by1', '1440.ce1', '2160.j1', '2160.ba1', '2160.bb1', '2160.bc1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [442641386755, 277050, 442162067904, 80880, 80787], 'label': '77760.bo.720.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '720.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.r1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246054956
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.p1', '360.g1', '360.w1'], 'contains': ['1440.g1', '1440.cr1', '1440.dg1', '2160.m1', '2160.bd1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [280259486761, 193999276800, 40585, 482768881, 80880], 'label': '77760.bo.720.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '720.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.s1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246054957
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.l1', '240.d1', '240.q1', '360.f1', '360.h1', '360.br1'], 'contains': ['1440.d1', '1440.cs1', '1440.cx1', '2160.k1', '2160.be1', '2160.bf1', '2160.bg1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [183845, 88176216509, 80880, 80787, 113567005680], 'label': '77760.bo.720.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '720.t1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.t1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246054958
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.d1', '240.o1', '360.i1'], 'contains': ['1440.e1', '1440.ct1', '1440.dc1', '2160.l1', '2160.bf1', '2160.bg1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [40349, 482849425, 280259701194, 193999455812, 80787], 'label': '77760.bo.720.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.i1', 'old_label': '720.u1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.u1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246054959
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.d1', '240.p1', '360.j1', '360.y1'], 'contains': ['1440.f1', '1440.cu1', '1440.de1', '2160.m1', '2160.bf1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [183845, 482635561, 280259665445, 80787, 193999357587], 'label': '77760.bo.720.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '720.v1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.v1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246054960
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.r1', '360.v1', '360.w1'], 'contains': ['1440.c1', '1440.g1', '1440.n1', '2160.n1', '2160.bh1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [280259567405, 143975, 193999277493, 85805, 143304], 'label': '77760.bo.720.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '720.w1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.w1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 246054961
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '40.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '20.b1', '20.c1', '20.e1'], 'contains': ['80.b1', '80.o1', '80.q1', '120.d1', '120.o1', '360.bh1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [280259521949, 88695170185, 482635561, 143975, 193999455812, 85805, 80880, 80787], 'label': '77760.bo.40.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.d1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246054962
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.r1', '360.x1', '360.y1'], 'contains': ['1440.f1', '1440.j1', '2160.n1', '2160.bi1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [193999357894, 280259567405, 85805, 80787, 693], 'label': '77760.bo.720.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '720.x1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.x1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 246054963
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.n1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.ba1', '240.e1', '240.g1', '360.z1', '360.be1', '360.bp1'], 'contains': ['1440.h1', '1440.q1', '1440.bo1', '2160.p1', '2160.r1', '2160.bj1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [518964004, 442641024148, 85805, 80880, 80787], 'label': '77760.bo.720.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '720.y1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.y1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246054964
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.n1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.bb1', '240.e1', '240.f1', '360.ba1'], 'contains': ['1440.i1', '1440.r1', '1440.bq1', '2160.q1', '2160.bj1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [183845, 174436599746, 143975, 375138172555, 80787], 'label': '77760.bo.720.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.f1', 'old_label': '720.z1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.z1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246054965
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gk1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.e1', '240.h1', '360.bb1', '360.bb2', '360.bc1', '360.bc2', '360.bs1'], 'contains': ['1440.a1', '1440.s1', '1440.br1', '2160.o1', '2160.bj1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [442641386424, 143975, 85805, 80880, 80787], 'label': '77760.bo.720.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '720.ba1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ba1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055102
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.fn2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.bb2', '360.cq2', '360.cx1', '360.ei1'], 'contains': ['1440.br1', '1440.cz1', '2160.gi2'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [442641300482, 143975, 80880, 80787, 448908283914], 'label': '77760.bo.720.fn2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '720.fn2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.fn2', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246054966
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.bd1', '240.f1', '240.g1', '240.h1', '360.bd1', '360.be1', '360.bq1'], 'contains': ['1440.h1', '1440.v1', '1440.by1', '2160.s1', '2160.t1', '2160.bj1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 80, 'diagramx': None, 'generators': [442641024148, 442162067904, 85805, 80880, 80787], 'label': '77760.bo.720.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '720.bb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bb1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246054967
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.a1', '240.i1', '360.bc1', '360.bc2', '360.bf1', '360.bf2', '360.bg1', '360.bh1', '360.bi1', '360.bj1', '360.bk1', '360.bo1', '360.bt1'], 'contains': ['1440.a1', '1440.be1', '1440.cp1', '2160.u1', '2160.bk1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [143975, 85805, 80880, 80787, 274467916948], 'label': '77760.bo.720.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '720.bc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bc1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246054968
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.e1', '180.bs1', '240.i1', '240.j1', '360.be1', '360.bl1', '360.br1'], 'contains': ['1440.h1', '1440.bf1', '1440.cs1', '2160.v1', '2160.w1', '2160.bk1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [183845, 143975, 442637676988, 80787, 368392188092], 'label': '77760.bo.720.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '720.bd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bd1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246054969
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.n1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.bj1', '240.k1', '240.l1', '240.m1', '360.bd1', '360.bl1', '360.bp1'], 'contains': ['1440.h1', '1440.bk1', '1440.bz1', '2160.x1', '2160.y1', '2160.bl1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [183845, 174436554242, 143975, 375138270474, 80787], 'label': '77760.bo.720.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '720.be1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.be1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246054970
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.bk1', '240.l1', '240.n1', '360.z1', '360.bl1', '360.bq1'], 'contains': ['1440.h1', '1440.bn1', '1440.ce1', '2160.z1', '2160.bb1', '2160.bl1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [183845, 442641386755, 143975, 442162022400, 80787], 'label': '77760.bo.720.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '720.bf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bf1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246054971
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.bl1', '240.k1', '240.n1', '360.ba1'], 'contains': ['1440.i1', '1440.bp1', '1440.cf1', '2160.bc1', '2160.bl1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [183845, 442641386755, 143975, 442162067904, 80787], 'label': '77760.bo.720.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.g1', 'old_label': '720.bg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bg1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246054972
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '40.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['20.a1', '20.e1'], 'contains': ['80.b1', '80.p1', '80.q1', '120.e1', '120.p1', '360.bi1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [183845, 88695170185, 143975, 280259700485, 193999455812, 482768881, 80880, 80787], 'label': '77760.bo.40.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.e1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246054973
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gk1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.m1', '240.n1', '360.bb1', '360.bb2', '360.bf1', '360.bf2', '360.bs1'], 'contains': ['1440.a1', '1440.br1', '1440.cg1', '2160.ba1', '2160.bl1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [183845, 442641386755, 143975, 80880, 80787], 'label': '77760.bo.720.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '720.bh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bh1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246054974
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.bo1', '240.o1', '240.p1', '240.q1', '360.z1', '360.bd1', '360.br1'], 'contains': ['1440.h1', '1440.cn1', '1440.cx1', '2160.bd1', '2160.bf1', '2160.bm1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [183845, 113566924800, 88176350010, 143975, 80787], 'label': '77760.bo.720.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '720.bi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bi1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246054975
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.bp1', '240.o1', '240.q1', '360.ba1'], 'contains': ['1440.i1', '1440.co1', '1440.cy1', '2160.bg1', '2160.bm1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [183845, 88176350010, 143975, 80787, 113567005680], 'label': '77760.bo.720.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ba1', 'old_label': '720.bj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bj1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246054976
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.b1', '240.q1', '360.bb1', '360.bb2', '360.bk1', '360.bt1'], 'contains': ['1440.a1', '1440.cp1', '1440.cz1', '2160.be1', '2160.bm1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [274468060348, 143975, 85805, 80880, 80787], 'label': '77760.bo.720.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '720.bk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bk1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246054977
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.bu1', '240.r1', '240.s1', '360.bp1', '360.bq1', '360.br1'], 'contains': ['1440.d1', '1440.h1', '1440.k1', '2160.bh1', '2160.bi1', '2160.bn1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [85805, 194518275844, 80880, 80787, 143304], 'label': '77760.bo.720.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '720.bl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bl1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246054978
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.t1', '240.u1', '360.x1', '360.bu1', '360.bv1'], 'contains': ['1440.j1', '1440.z1', '1440.cd1', '2160.bo1', '2160.bp1', '2160.bq1', '2160.br1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [174400208787, 93448938387, 456053150130, 45813, 80787], 'label': '77760.bo.720.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.r1', 'old_label': '720.bm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246054979
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.v1', '240.w1', '360.y1', '360.bv1', '360.bw1', '360.bx1', '360.by1'], 'contains': ['1440.j1', '1440.bh1', '1440.de1', '2160.bs1', '2160.bt1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [482808988, 280259481600, 224184, 193999500984, 80787], 'label': '77760.bo.720.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '720.bn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bn1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246054980
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.x1', '360.x1', '360.bu1', '360.bw1'], 'contains': ['1440.j1', '1440.bu1', '2160.bu1', '2160.bv1', '2160.bw1', '2160.bx1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [174400208787, 93448938387, 456053154955, 80787, 693], 'label': '77760.bo.720.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.r1', 'old_label': '720.bo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bo1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246054981
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.y1', '360.y1', '360.bu1'], 'contains': ['1440.j1', '1440.cu1', '2160.by1', '2160.bz1', '2160.ca1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [280259481600, 482849425, 193999455627, 80787, 143304], 'label': '77760.bo.720.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '720.bp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bp1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246054982
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.t1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.cc1', '240.t1', '240.z1', '360.bp1', '360.bz1', '360.cd1'], 'contains': ['1440.k1', '1440.q1', '1440.bz1', '2160.bo1', '2160.cb1', '2160.cd1', '2160.ce1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [224184, 143975, 174436559403, 80787, 375138230375], 'label': '77760.bo.720.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '720.bq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246054983
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '40.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['20.d1'], 'contains': ['80.a1', '80.c1', '80.e1', '80.f1', '80.h1', '120.q1', '120.s1', '120.t1'], 'core': '720.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [456053074316, 93449001331, 143975, 174400173363, 85805, 80880, 80787, 143304], 'label': '77760.bo.40.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '40.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.f1', 'subgroup_fusion': None, 'weyl_group': '1296.2985'}
  • id: 246054984
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.cd1', '240.u1', '240.z1', '360.ce1'], 'contains': ['1440.l1', '1440.t1', '1440.ca1', '2160.bo1', '2160.cc1', '2160.cf1', '2160.cg1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [224184, 375138311012, 174436559403, 80787, 179159], 'label': '77760.bo.720.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ce1', 'old_label': '720.br1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.br1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246054985
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.ba1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.ce1', '240.t1', '240.ba1', '360.bq1', '360.ca1', '360.cd1'], 'contains': ['1440.k1', '1440.v1', '1440.ce1', '2160.bp1', '2160.cb1', '2160.ch1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [442641386187, 143975, 442162022400, 80787, 143304], 'label': '77760.bo.720.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '720.bs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bs1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246054986
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.cf1', '240.u1', '240.ba1', '360.ce1'], 'contains': ['1440.l1', '1440.w1', '1440.ch1', '2160.bp1', '2160.cc1', '2160.ci1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [442641386284, 442162022400, 80787, 143304, 179159], 'label': '77760.bo.720.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.x1', 'old_label': '720.bt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bt1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246054987
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.t1', '360.cb1'], 'contains': ['1440.m1', '1440.ba1', '1440.cj1', '2160.bq1', '2160.ce1', '2160.ch1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [83462998, 174400208880, 148, 93448902963, 693], 'label': '77760.bo.720.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.v1', 'old_label': '720.bu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bu1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246054988
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.t1', '360.v1', '360.cc1', '360.cf1'], 'contains': ['1440.n1', '1440.bb1', '1440.ck1', '2160.br1', '2160.cd1', '2160.ch1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [93449082115, 224184, 83462998, 174400128000, 224515], 'label': '77760.bo.720.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '720.bv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bv1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246054989
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.u1'], 'contains': ['1440.o1', '1440.bc1', '1440.cl1', '2160.bq1', '2160.cg1', '2160.ci1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [174400208787, 93449001331, 178680, 83462998, 179159], 'label': '77760.bo.720.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.u1', 'old_label': '720.bw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bw1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246054990
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.u1', '360.cg1'], 'contains': ['1440.p1', '1440.bd1', '1440.cm1', '2160.br1', '2160.cf1', '2160.ci1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [178680, 456053069398, 174400128000, 93449036759, 179159], 'label': '77760.bo.720.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.x1', 'old_label': '720.bx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bx1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246054991
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.g1', '180.cn1', '240.v1', '240.bb1', '360.br1', '360.cd1', '360.ch1'], 'contains': ['1440.k1', '1440.bf1', '1440.cx1', '2160.bs1', '2160.cj1', '2160.cl1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [88176292437, 113566924800, 178680, 143975, 80787], 'label': '77760.bo.720.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '720.by1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.by1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246054992
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.h1', '180.co1', '240.w1', '240.bb1', '360.ce1'], 'contains': ['1440.l1', '1440.bg1', '1440.da1', '2160.bs1', '2160.ck1', '2160.cm1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [80787, 442637676744, 143304, 179159, 368392228437], 'label': '77760.bo.720.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ce1', 'old_label': '720.bz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bz1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246054993
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.v1', '360.w1', '360.cf1', '360.ck1', '360.cl1', '360.cm1'], 'contains': ['1440.n1', '1440.bi1', '1440.dg1', '2160.bt1', '2160.cl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [280259481600, 482854584, 224184, 224515, 193999277398], 'label': '77760.bo.720.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '720.ca1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ca1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246054994
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '40.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.d1', '20.e1'], 'contains': ['80.b1', '80.d1', '80.e1', '80.g1', '80.i1', '120.r1', '120.u1'], 'core': '720.a1', 'coset_action_label': None, 'count': 10, 'diagramx': None, 'generators': [193999357894, 280259521949, 143975, 482768881, 85805, 80880, 80787, 143304], 'label': '77760.bo.40.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.g1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246054995
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.w1', '360.cg1', '360.cn1'], 'contains': ['1440.p1', '1440.bj1', '1440.dh1', '2160.bt1', '2160.cm1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [280259481600, 482854584, 224184, 193999277493, 224612], 'label': '77760.bo.720.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.s1', 'old_label': '720.cb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.cb1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246054996
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.n1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.cj1', '240.x1', '240.bc1', '360.bp1', '360.ca1', '360.ch1'], 'contains': ['1440.k1', '1440.bk1', '1440.bo1', '2160.bu1', '2160.cn1', '2160.co1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [518964004, 442641109705, 80880, 80787, 143304], 'label': '77760.bo.720.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '720.cc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.cc1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246054997
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.x1', '360.cb1'], 'contains': ['1440.m1', '1440.bl1', '1440.bw1', '2160.bv1', '2160.cn1', '2160.cq1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [83548555, 174400208787, 93449036612, 143975, 143304], 'label': '77760.bo.720.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.cb1', 'old_label': '720.cd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.cd1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246054998
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.x1', '360.v1', '360.cc1', '360.ck1'], 'contains': ['1440.n1', '1440.bm1', '1440.bx1', '2160.bw1', '2160.cn1', '2160.cp1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [456053154955, 174400128000, 143975, 93449001575, 143304], 'label': '77760.bo.720.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '720.ce1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ce1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246054999
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.ck1', '240.x1', '240.bd1', '360.bq1', '360.bz1', '360.ch1'], 'contains': ['1440.k1', '1440.bn1', '1440.by1', '2160.bx1', '2160.co1', '2160.cp1', '2160.cq1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [178680, 442641300482, 143975, 442162022400, 80787], 'label': '77760.bo.720.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '720.cf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.cf1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246055000
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.cl1', '240.y1', '240.be1', '360.br1', '360.bz1', '360.ca1'], 'contains': ['1440.k1', '1440.cn1', '1440.cs1', '2160.by1', '2160.cr1', '2160.cs1', '2160.ct1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [113566924800, 88176252092, 143975, 80787, 143304], 'label': '77760.bo.720.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '720.cg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.cg1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246055001
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.y1', '360.cb1'], 'contains': ['1440.m1', '1440.cq1', '1440.cv1', '2160.bz1', '2160.cs1', '2160.ct1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [280259481843, 193999455627, 482768881, 80880, 143304], 'label': '77760.bo.720.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.cb1', 'old_label': '720.ch1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ch1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246055002
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.y1', '360.w1', '360.cc1'], 'contains': ['1440.n1', '1440.cr1', '1440.cw1', '2160.ca1', '2160.cs1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [280259481600, 482849425, 143975, 193999277493, 143304], 'label': '77760.bo.720.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '720.ci1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ci1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246055003
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.ga1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.z1', '240.ba1', '360.bs1', '360.co1', '360.co2', '360.cp1', '360.cp2'], 'contains': ['1440.b1', '1440.s1', '1440.cg1', '2160.cb1', '2160.cc1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [442641386424, 143975, 80880, 80787, 143304], 'label': '77760.bo.720.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '720.cj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.cj1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055004
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1', '240.bb1', '360.bt1', '360.cp1', '360.cp2', '360.cq1', '360.cq2', '360.cr1', '360.cs1', '360.ct1', '360.cu1', '360.cv1', '360.cw1'], 'contains': ['1440.b1', '1440.be1', '1440.cz1', '2160.cj1', '2160.ck1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [143975, 80880, 80787, 274467916948, 143304], 'label': '77760.bo.720.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '720.ck1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ck1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055005
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '40.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['20.d1'], 'contains': ['80.f1', '80.h1', '80.i1', '80.j1', '80.r1', '120.v1', '120.bc1', '120.bd1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [93449001331, 83467916, 143975, 174400173363, 180587272349, 80880, 80787, 143304], 'label': '77760.bo.40.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '40.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.h1', 'subgroup_fusion': None, 'weyl_group': '3888.ik'}
  • id: 246055006
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gk1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.bc1', '240.bd1', '360.bs1', '360.co1', '360.co2', '360.cq1', '360.cq2'], 'contains': ['1440.b1', '1440.br1', '2160.co1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [442641300482, 143975, 80880, 80787, 143304], 'label': '77760.bo.720.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '720.cl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.cl1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055007
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1', '240.be1', '360.bt1', '360.co1', '360.co2', '360.cr1'], 'contains': ['1440.b1', '1440.cp1', '2160.cr1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [143975, 274468002505, 80880, 80787, 143304], 'label': '77760.bo.720.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '720.cm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.cm1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055008
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.dq1', '240.bf1', '240.bi1', '360.k1', '360.z1', '360.bz1'], 'contains': ['1440.q1', '1440.bn1', '1440.cn1', '2160.cu1', '2160.cv1', '2160.cw1', '2160.cy1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [442641386187, 143975, 998139594, 519235320, 80787], 'label': '77760.bo.720.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '720.cn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.cn1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055009
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.dr1', '240.bf1', '240.bh1', '360.ba1'], 'contains': ['1440.r1', '1440.bp1', '1440.co1', '2160.cu1', '2160.cz1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [174436559876, 80880, 80787, 368871154316, 375138086400], 'label': '77760.bo.720.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ba1', 'old_label': '720.co1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.co1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055010
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.bf1', '240.bj1', '360.bb1', '360.bc1', '360.co1', '360.cx1', '360.cx3', '360.cy1', '360.cy2'], 'contains': ['1440.s1', '1440.br1', '1440.cp1', '2160.cu1', '2160.cx1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [442641386424, 143975, 443120066492, 80880, 80787], 'label': '77760.bo.720.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.x1', 'old_label': '720.cp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.cp1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055011
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.cp2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.bb2', '360.bc2', '360.co2', '360.cx1', '360.cx2', '360.cy1', '360.cy2'], 'contains': ['1440.s1', '1440.br1', '1440.cp1', '2160.cu2', '2160.cx2'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [448908283441, 442641386424, 143975, 80880, 80787], 'label': '77760.bo.720.cp2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '720.cp2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.cp2', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055012
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.dt1', '240.bf1', '240.bk1', '360.f1', '360.be1', '360.bz1'], 'contains': ['1440.q1', '1440.by1', '1440.cs1', '2160.cx1', '2160.cy1', '2160.cz1', '2160.da1', '2160.db1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [442641386187, 997925759, 143975, 519235320, 80787], 'label': '77760.bo.720.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '720.cq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.cq1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246055013
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.du1', '240.bg1', '240.bm1', '360.f1', '360.z1', '360.cd1'], 'contains': ['1440.q1', '1440.ce1', '1440.cx1', '2160.dc1', '2160.de1', '2160.df1', '2160.dh1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [442641386187, 143975, 997965813, 519235320, 80787], 'label': '77760.bo.720.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '720.cr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.cr1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055014
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.dv1', '240.bg1', '240.bl1', '360.ba1'], 'contains': ['1440.r1', '1440.cf1', '1440.cy1', '2160.dc1', '2160.df1', '2160.dg1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [442641386187, 143975, 997965813, 80787, 519235228], 'label': '77760.bo.720.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ba1', 'old_label': '720.cs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.cs1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055015
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.bg1', '240.bn1', '360.bb1', '360.cp1', '360.cx1', '360.da1', '360.da2'], 'contains': ['1440.s1', '1440.cg1', '1440.cz1', '2160.dc1', '2160.dd1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [442641386424, 143975, 443120071554, 80880, 80787], 'label': '77760.bo.720.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.x1', 'old_label': '720.ct1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ct1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055016
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '40.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['20.d1', '20.f1', '20.g1'], 'contains': ['80.f1', '80.g1', '80.k1', '80.l1', '80.n1', '120.w1', '120.x1', '120.be1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [180587277504, 93449001331, 143975, 174400173363, 456053150130, 80880, 80787, 143304], 'label': '77760.bo.40.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.i1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246055017
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.ct2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.bb2', '360.cp2', '360.cx2', '360.cx3', '360.da1', '360.da2'], 'contains': ['1440.s1', '1440.cg1', '1440.cz1', '2160.dc2', '2160.dd2'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [442641386755, 143975, 448908278667, 80880, 80787], 'label': '77760.bo.720.ct2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '720.ct2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ct2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055018
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.dx1', '240.bg1', '240.bp1', '360.ce1'], 'contains': ['1440.t1', '1440.ch1', '1440.da1', '2160.dd1', '2160.de1', '2160.dg1', '2160.di1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [174436496787, 375138311012, 368871230130, 80787, 179159], 'label': '77760.bo.720.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ce1', 'old_label': '720.cu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.cu1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055019
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.dy1', '240.bg1', '240.bo1'], 'contains': ['1440.u1', '1440.ci1', '1440.db1', '2160.dd1', '2160.df1', '2160.dg1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [375138311012, 368871230130, 174436416243, 80787, 179159], 'label': '77760.bo.720.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '720.cv1', 'old_label': '720.cv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.cv1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 246055020
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.bq1', '360.bc1', '360.cp1', '360.cy2', '360.cz1', '360.da2', '360.db1', '360.dc1', '360.dd1', '360.dh1', '360.di1', '360.dl1'], 'contains': ['1440.s1', '1440.be1', '2160.dj1', '2160.dk1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [143975, 87182201788, 80880, 80787, 375138230375], 'label': '77760.bo.720.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '720.cw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.cw1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055021
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.cw2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.bc2', '360.cp2', '360.cy1', '360.da1', '360.de1', '360.df1', '360.dg1', '360.dl1'], 'contains': ['1440.s1', '1440.be1', '2160.dj2', '2160.dk2'], 'core': '2880.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [143975, 448908278667, 80787, 442641386424, 80880], 'label': '77760.bo.720.cw2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '720.cw2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.cw2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055022
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.dz1', '240.bh1', '240.bi1', '240.bj1', '360.k1', '360.bd1', '360.ca1'], 'contains': ['1440.v1', '1440.bk1', '1440.cn1', '2160.cu1', '2160.dl1', '2160.dm1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [518964004, 997965504, 442641300958, 80880, 80787], 'label': '77760.bo.720.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '720.cx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.cx1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055023
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.bi1', '360.cb1'], 'contains': ['1440.ba1', '1440.bl1', '1440.cq1', '2160.cw1', '2160.dl1', '2160.do1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [93449036612, 174400128000, 224515, 456053293315, 180587272349], 'label': '77760.bo.720.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.cb1', 'old_label': '720.cy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.cy1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055025
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.ea1', '240.bj1', '240.bk1', '360.h1', '360.be1', '360.ca1'], 'contains': ['1440.v1', '1440.bo1', '1440.cs1', '2160.cx1', '2160.dm1', '2160.dn1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [998099012, 143975, 519235320, 442641301050, 80787], 'label': '77760.bo.720.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '720.da1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.da1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246055026
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.bh1', '240.bk1', '360.i1'], 'contains': ['1440.x1', '1440.bs1', '1440.ct1', '2160.cz1', '2160.dm1', '2160.dp1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [174400409788, 93449036612, 180587415845, 83462400, 80787], 'label': '77760.bo.720.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.g1', 'old_label': '720.db1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.db1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246055027
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '40.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['20.d1', '20.f1', '20.h1'], 'contains': ['80.g1', '80.h1', '80.m1', '80.s1', '120.y1', '120.bf1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [180587277504, 456053074316, 93449001331, 143975, 174400173363, 80880, 80787, 143304], 'label': '77760.bo.40.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.j1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246055028
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.bi1', '240.bk1', '360.j1', '360.l1', '360.bu1'], 'contains': ['1440.z1', '1440.bu1', '1440.cu1', '2160.cy1', '2160.dm1', '2160.do1', '2160.dq1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [174400208787, 93448938387, 456053154955, 180587318155, 80787], 'label': '77760.bo.720.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '720.dc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.dc1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246055029
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.bk1', '360.cb1'], 'contains': ['1440.ba1', '1440.bw1', '1440.cv1', '2160.db1', '2160.dn1', '2160.do1', '2160.dp1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [180587451025, 174400208787, 93449036612, 179012, 456053154955], 'label': '77760.bo.720.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.cb1', 'old_label': '720.dd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.dd1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246055030
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.bk1', '360.a1', '360.m1', '360.cc1'], 'contains': ['1440.bb1', '1440.bx1', '1440.cw1', '2160.da1', '2160.dn1', '2160.dp1', '2160.dq1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [456053069043, 93448857748, 148, 180587272349, 174400128148], 'label': '77760.bo.720.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '720.de1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.de1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246055031
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.eb1', '240.bl1', '240.bm1', '240.bn1', '360.h1', '360.bd1', '360.cd1'], 'contains': ['1440.v1', '1440.bz1', '1440.cx1', '2160.dc1', '2160.dr1', '2160.ds1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [442641386755, 998099012, 143975, 519235320, 80787], 'label': '77760.bo.720.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '720.df1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.df1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055032
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.ec1', '240.bn1', '240.bo1', '240.bp1', '360.ce1'], 'contains': ['1440.w1', '1440.ca1', '1440.da1', '2160.dd1', '2160.dr1', '2160.dt1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [174436496787, 375138087093, 368871373412, 80787, 179159], 'label': '77760.bo.720.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ce1', 'old_label': '720.dg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.dg1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055033
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.bl1', '240.bm1', '240.bo1', '360.i1'], 'contains': ['1440.x1', '1440.cb1', '1440.dc1', '2160.df1', '2160.dr1', '2160.du1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [180587277813, 93448938387, 174400307012, 456053150130, 80787], 'label': '77760.bo.720.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.i1', 'old_label': '720.dh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.dh1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055034
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.bl1', '240.bo1', '240.bp1'], 'contains': ['1440.y1', '1440.cc1', '1440.dd1', '2160.dg1', '2160.dr1', '2160.dv1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [180587456184, 174400352612, 93449174667, 83462400, 80787], 'label': '77760.bo.720.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '720.di1', 'old_label': '720.di1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.di1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055035
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.bm1', '240.bp1', '360.j1', '360.bv1'], 'contains': ['1440.z1', '1440.cd1', '1440.de1', '2160.de1', '2160.dr1', '2160.dw1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [174400208787, 180587277813, 93448938387, 456053150130, 80787], 'label': '77760.bo.720.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.r1', 'old_label': '720.dj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.dj1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055036
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.bm1', '360.a1', '360.g1', '360.cf1'], 'contains': ['1440.bb1', '1440.ck1', '1440.dg1', '2160.dh1', '2160.ds1', '2160.du1', '2160.dw1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [180587456184, 93449082115, 174400128000, 224515, 83686915], 'label': '77760.bo.720.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '720.dk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.dk1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246055037
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.bp1', '360.cg1'], 'contains': ['1440.bd1', '1440.cm1', '1440.dh1', '2160.di1', '2160.dt1', '2160.dv1', '2160.dw1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [180587410680, 456053069398, 174400128000, 93449036759, 179159], 'label': '77760.bo.720.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.x1', 'old_label': '720.dl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.dl1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246055038
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '40.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '20.e1', '20.g1', '20.h1'], 'contains': ['80.g1', '80.o1', '80.p1', '120.z1', '120.bb1', '360.ct1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 10, 'diagramx': None, 'generators': [482808988, 193999357894, 143975, 88695353644, 280259527104, 80880, 80787, 143304], 'label': '77760.bo.40.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.k1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246055039
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.k1', '180.ee1', '240.bq1', '240.br1', '360.k1', '360.be1', '360.cd1'], 'contains': ['1440.q1', '1440.v1', '1440.bf1', '2160.dj1', '2160.dx1', '2160.dy1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [442641386187, 998099012, 143975, 519235320, 80787], 'label': '77760.bo.720.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '720.dm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.dm1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055040
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.l1', '180.ef1', '240.bq1', '240.bs1', '360.ce1'], 'contains': ['1440.t1', '1440.w1', '1440.bg1', '2160.dk1', '2160.dx1', '2160.dz1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [519235467, 998063731, 442641386284, 80787, 179159], 'label': '77760.bo.720.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.be1', 'old_label': '720.dn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.dn1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055041
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.br1', '240.bs1', '360.l1', '360.bv1', '360.dr1', '360.dt1', '360.dw1'], 'contains': ['1440.z1', '1440.bh1', '2160.dx1', '2160.ea1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [456053068800, 174400208787, 93448938387, 180587232000, 80787], 'label': '77760.bo.720.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '720.do1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.do1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246055042
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.br1', '360.b1', '360.m1', '360.cf1', '360.dq1', '360.ds1', '360.du1', '360.dx1'], 'contains': ['1440.bb1', '1440.bi1', '2160.dy1', '2160.ea1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [180587277504, 456053114304, 174400208880, 93448938480, 80880], 'label': '77760.bo.720.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '720.dp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.dp1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246055043
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.bs1', '360.cg1', '360.dv1', '360.dy1'], 'contains': ['1440.bd1', '1440.bj1', '2160.dz1', '2160.ea1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [83641559, 174400128000, 93449036759, 180587232000, 179159], 'label': '77760.bo.720.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.s1', 'old_label': '720.dq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.dq1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246055062
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.p1', '180.fb1', '240.bu1', '240.bz1', '360.ce1'], 'contains': ['1440.bg1', '1440.ca1', '1440.ch1', '2160.ee1', '2160.ey1', '2160.fa1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [375138167730, 174436496787, 368871230130, 80787, 179159], 'label': '77760.bo.720.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ce1', 'old_label': '720.ee1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ee1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055044
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.bt1', '360.bc1', '360.bf1', '360.cq1', '360.cy1', '360.cz1', '360.dz2', '360.ea1', '360.eb1', '360.ec1', '360.ed1', '360.ei1', '360.ej1', '360.ek1', '360.ey1', '360.fb1'], 'contains': ['1440.be1', '1440.br1', '2160.eb1', '2160.ec1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 375138270474, 87182201788, 80880, 80787], 'label': '77760.bo.720.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '720.dr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.dr1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246055045
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.dr2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.bc2', '360.bf2', '360.cq2', '360.cy2', '360.dz1', '360.ee1', '360.ef1', '360.eg1', '360.eh1', '360.ei1', '360.fb1'], 'contains': ['1440.be1', '1440.br1', '2160.eb2', '2160.ec2'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [143975, 442641300958, 80880, 80787, 448908283914], 'label': '77760.bo.720.dr2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '720.dr2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.dr2', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055046
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.bu1', '360.bf1', '360.cp1', '360.da1', '360.db1', '360.dz1', '360.ea1', '360.el1', '360.em1', '360.eq1', '360.fh1', '360.fk1'], 'contains': ['1440.be1', '1440.cg1', '2160.ed1', '2160.ee1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [375138087093, 143975, 87182201788, 80880, 80787], 'label': '77760.bo.720.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '720.ds1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ds1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055047
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.ds2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.bf2', '360.cp2', '360.da2', '360.dz2', '360.en1', '360.eo1', '360.ep1', '360.fk1'], 'contains': ['1440.be1', '1440.cg1', '2160.ed2', '2160.ee2'], 'core': '2880.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [448908278999, 442641386755, 143975, 80880, 80787], 'label': '77760.bo.720.ds2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '720.ds2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ds2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055048
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.bk1', '360.bo1', '360.cr1', '360.cy1', '360.cy2', '360.dc1', '360.dz1', '360.dz2', '360.eb1', '360.ec1', '360.el1', '360.er1', '360.es1', '360.et1', '360.fn1'], 'contains': ['1440.be1', '1440.cp1', '2160.ef1', '2160.eg1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 274468100401, 268244570163, 80880, 80787], 'label': '77760.bo.720.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '720.dt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.dt1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246055049
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '40.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.e1', '20.f1'], 'contains': ['80.g1', '80.q1', '120.ba1', '360.cu1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 10, 'diagramx': None, 'generators': [143975, 80787, 143304, 280259527104, 88695348625, 80880, 193999357894, 482808988], 'label': '77760.bo.40.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.l1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246055050
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.bk1', '360.cw1', '360.da1', '360.da2', '360.dd1', '360.ed1', '360.ei1', '360.em1', '360.er1', '360.eu1', '360.fr1'], 'contains': ['1440.be1', '1440.cz1', '2160.eh1', '2160.ei1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [274468060348, 143975, 268244570163, 80880, 80787], 'label': '77760.bo.720.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '720.du1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.du1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055051
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.f1', '360.bg1', '360.cs1', '360.de1', '360.dh1', '360.eb1', '360.ee1', '360.em1', '360.en1'], 'contains': ['1440.be1', '2160.ej1', '2160.er1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [443120250115, 143975, 267845673628, 80880, 80787], 'label': '77760.bo.720.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '720.dv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.dv1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055052
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.o1', '360.bh1', '360.ct1', '360.de1', '360.di1', '360.ef1', '360.ej1', '360.eo1', '360.eq1', '360.es1', '360.eu1', '360.fu1'], 'contains': ['1440.be1', '2160.ek1', '2160.es1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [482711044, 88695175204, 143975, 80880, 80787], 'label': '77760.bo.720.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '720.dw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.dw1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055053
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.p1', '360.bi1', '360.ct1', '360.db1', '360.df1', '360.eg1', '360.ek1', '360.en1', '360.et1', '360.fr1'], 'contains': ['1440.be1', '2160.el1', '2160.et1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [482711044, 143975, 88695353644, 80880, 80787], 'label': '77760.bo.720.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '720.dx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.dx1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055054
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.q1', '360.bh1', '360.bi1', '360.cu1', '360.cz1', '360.dg1', '360.ea1', '360.ee1', '360.eh1', '360.ep1', '360.er1', '360.fn1'], 'contains': ['1440.be1', '2160.em1', '2160.en1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [482711044, 88695170185, 143975, 80880, 80787], 'label': '77760.bo.720.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '720.dy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.dy1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246055055
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.g1', '360.bg1', '360.bj1', '360.cv1', '360.dc1', '360.dg1', '360.ed1', '360.ef1', '360.eg1', '360.el1', '360.ep1', '360.ey1'], 'contains': ['1440.be1', '2160.eo1', '2160.ep1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [143975, 80787, 267845678885, 443120250115, 80880], 'label': '77760.bo.720.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '720.dz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.dz1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246055056
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.h1', '360.bj1', '360.cs1', '360.dd1', '360.df1', '360.ec1', '360.eh1', '360.eo1', '360.fh1'], 'contains': ['1440.be1', '2160.eq1', '2160.eu1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [443120250115, 143975, 80880, 80787, 267845674052], 'label': '77760.bo.720.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '720.ea1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ea1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055057
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.m1', '180.ey1', '240.bt1', '240.bw1', '360.k1', '360.bl1', '360.ch1'], 'contains': ['1440.bf1', '1440.bk1', '1440.bn1', '2160.eb1', '2160.ev1', '2160.ew1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [442641300629, 143975, 998139594, 519235320, 80787], 'label': '77760.bo.720.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '720.eb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.eb1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055058
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.n1', '180.ez1', '240.bt1', '240.bx1', '360.n1', '360.be1', '360.ch1'], 'contains': ['1440.bf1', '1440.bo1', '1440.by1', '2160.ec1', '2160.ew1', '2160.ex1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [997925759, 143975, 519235320, 442641301050, 80787], 'label': '77760.bo.720.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '720.ec1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ec1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246055059
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.o1', '180.fa1', '240.bu1', '240.by1', '360.n1', '360.bl1', '360.cd1'], 'contains': ['1440.bf1', '1440.bz1', '1440.ce1', '2160.ed1', '2160.ey1', '2160.ez1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [442641386852, 143975, 997965813, 519235320, 80787], 'label': '77760.bo.720.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '720.ed1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ed1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055060
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': ['19440.a1', '19440.j1', '19440.j2', '19440.d1', '19440.z1', '19440.i1', '19440.e1', '19440.y1', '19440.h1', '19440.y2'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '2.d1'], 'contains': ['8.a1', '12.n1', '12.o1', '24.f1', '40.s1', '60.bj1'], 'core': '4.e1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [462320323891, 143975, 93924409412, 80880, 80787], 'label': '77760.bo.4.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': ['2.b1', '2.d1'], 'normal_contains': ['8.a1'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '77760.bo', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': '25920.w'}
  • id: 246055061
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '40.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['20.a1', '20.b1', '20.f1'], 'contains': ['80.l1', '80.m1', '80.q1', '120.bj1', '120.bk1', '360.cz1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [180587277504, 83601118, 93449001331, 143975, 174400173363, 456053248051, 80880, 80787], 'label': '77760.bo.40.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.m1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246055063
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['144.i1', '240.bv1', '360.o1', '360.bm1', '360.ci1', '360.dj1', '360.do1', '360.ev1', '360.ew1', '360.ez1', '360.fc1', '360.fd1', '360.ff1', '360.fl1', '360.fo1', '360.fp1', '360.gg1'], 'contains': ['2160.fb1', '2160.fd1', '2160.fe1', '2160.fg1', '2160.fh1', '2880.b1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [274467962404, 143975, 194518339175, 268244605587, 80787], 'label': '77760.bo.720.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '720.ef1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ef1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246055064
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.bv1', '360.bn1', '360.dk1', '360.ex1', '360.fa1', '360.fg1', '360.fm1', '360.fq1'], 'contains': ['2160.fb1', '2160.fe1', '2160.ff1', '2880.c1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [355499101444, 355419504028, 442681021680, 80880, 80787], 'label': '77760.bo.720.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1', 'old_label': '720.eg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.eg1', 'subgroup_fusion': None, 'weyl_group': '432.747'}
  • id: 246055065
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.bv1', '360.bo1', '360.cw1', '360.dh1', '360.dl1', '360.ey1', '360.fb1', '360.fh1', '360.fk1', '360.fn1', '360.fr1', '360.fu1'], 'contains': ['1440.be1', '2160.fb1', '2160.fc1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [355499200051, 143975, 442681021680, 80880, 80787], 'label': '77760.bo.720.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '720.eh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.eh1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246055066
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.j1', '240.bv1', '360.cj1', '360.dm1', '360.dp1', '360.fe1', '360.fi1', '360.fs1', '360.gh1'], 'contains': ['2160.fc1', '2160.fd1', '2160.ff1', '2160.fi1', '2160.fj1', '2880.d1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [274467962404, 268244605587, 194518419812, 80787, 179159], 'label': '77760.bo.720.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.k1', 'old_label': '720.ei1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ei1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246055067
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.bv1', '360.dn1', '360.fj1', '360.ft1'], 'contains': ['2160.fc1', '2160.fe1', '2160.ff1', '2880.e1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [274467962404, 194518374451, 268244605587, 80787, 179159], 'label': '77760.bo.720.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.bb1', 'old_label': '720.ej1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ej1', 'subgroup_fusion': None, 'weyl_group': '216.165'}
  • id: 246055068
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.bw1', '360.b1', '360.p1', '360.ck1', '360.dq1', '360.fv1', '360.fw1', '360.fz1'], 'contains': ['1440.bi1', '1440.bm1', '2160.ev1', '2160.fk1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [93449082115, 456053207518, 174400128000, 224515, 180587232000], 'label': '77760.bo.720.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '720.ek1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ek1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246055069
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.bw1', '240.bx1', '360.l1', '360.q1', '360.bw1', '360.dr1', '360.fx1', '360.ga1', '360.gb1'], 'contains': ['1440.bh1', '1440.bu1', '2160.ew1', '2160.fk1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [174400208787, 93448938387, 456053073961, 180587232000, 80787], 'label': '77760.bo.720.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '720.el1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.el1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246055070
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.bx1', '360.c1', '360.m1', '360.ck1', '360.ds1', '360.fy1', '360.fz1', '360.gc1'], 'contains': ['1440.bi1', '1440.bx1', '2160.ex1', '2160.fk1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [180587232243, 93448857748, 456053073961, 148, 174400128148], 'label': '77760.bo.720.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '720.em1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.em1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246055071
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.by1', '240.bz1', '360.q1', '360.bv1', '360.dt1', '360.fx1', '360.gd1'], 'contains': ['1440.bh1', '1440.cd1', '2160.ey1', '2160.fl1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [174400208787, 93448938387, 456053150130, 180587232000, 80787], 'label': '77760.bo.720.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '720.en1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.en1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246055072
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '40.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['20.a1', '20.g1'], 'contains': ['80.l1', '80.n1', '80.p1', '120.bl1', '120.bm1', '360.db1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [180587277504, 93449001331, 83543730, 143975, 174400173363, 456053248051, 80880, 80787], 'label': '77760.bo.40.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.n1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246055073
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.by1', '360.c1', '360.p1', '360.cf1', '360.du1', '360.fv1', '360.fy1', '360.ge1'], 'contains': ['1440.bi1', '1440.ck1', '2160.ez1', '2160.fl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [180587232243, 93448857748, 456053069398, 148, 174400128148], 'label': '77760.bo.720.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '720.eo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.eo1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246055074
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.bz1', '360.cg1', '360.dv1', '360.gf1'], 'contains': ['1440.bj1', '1440.cm1', '2160.fa1', '2160.fl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [83462998, 174400128000, 93449036759, 180587232000, 179159], 'label': '77760.bo.720.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.s1', 'old_label': '720.ep1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ep1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246055075
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '240.ca1', '240.ce1', '360.r1', '360.bx1', '360.dw1', '360.ga1', '360.gd1'], 'contains': ['1440.bh1', '2160.fm1', '6480.cw1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 10, 'diagramx': None, 'generators': [280259481600, 482676004, 88695175204, 80787, 193999357587], 'label': '77760.bo.720.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '720.eq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.eq1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246055076
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.cb1', '240.cf1', '360.s1', '360.bx1', '360.dt1', '360.gb1'], 'contains': ['1440.bh1', '2160.fn1', '6480.cx1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [280259481600, 482676004, 88695353644, 80787, 193999357587], 'label': '77760.bo.720.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '720.er1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.er1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246055077
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.cc1', '240.cd1', '360.r1', '360.s1', '360.by1', '360.dr1', '360.fx1'], 'contains': ['1440.bh1', '2160.fo1', '6480.cy1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [280259481600, 482676004, 88695170185, 80787, 193999357587], 'label': '77760.bo.720.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '720.es1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.es1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246055078
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.q1', '240.ca1', '360.d1', '360.t1', '360.cl1', '360.dx1', '360.fw1', '360.gc1', '360.ge1'], 'contains': ['1440.bi1', '2160.fm1', '6480.dc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [280259481600, 88695129600, 482630400, 143975, 193999420775], 'label': '77760.bo.720.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '720.et1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.et1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246055079
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.cb1', '360.e1', '360.u1', '360.cl1', '360.du1', '360.fz1'], 'contains': ['1440.bi1', '2160.fn1', '6480.dd1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [482675904, 88695272904, 193999276800, 280259527104, 80880], 'label': '77760.bo.720.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '720.eu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.eu1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246055080
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.cc1', '360.d1', '360.u1', '360.cm1', '360.dq1', '360.fy1'], 'contains': ['1440.bi1', '2160.fo1', '6480.de1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [280259481600, 88695170185, 482630400, 143975, 193999420775], 'label': '77760.bo.720.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '720.ev1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ev1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246055081
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.cd1', '360.e1', '360.t1', '360.cm1', '360.ds1', '360.fv1'], 'contains': ['1440.bi1', '2160.fo1', '6480.df1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [482675904, 88695170185, 193999276800, 280259527104, 80880], 'label': '77760.bo.720.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '720.ew1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ew1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246055082
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.r1', '240.ce1', '360.cn1', '360.dy1', '360.gf1'], 'contains': ['1440.bj1', '2160.fm1', '6480.dk1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [280259481600, 88695129600, 193999455959, 482630400, 179159], 'label': '77760.bo.720.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.s1', 'old_label': '720.ex1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ex1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246055083
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '40.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '20.b1', '20.g1'], 'contains': ['80.l1', '80.o1', '120.bn1', '120.bo1', '360.di1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 10, 'diagramx': None, 'generators': [143975, 456053248051, 80787, 83641651, 174400173363, 180587277504, 93449001331, 80880], 'label': '77760.bo.40.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.o1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246055084
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.cf1', '360.cn1', '360.dv1'], 'contains': ['1440.bj1', '2160.fn1', '6480.dl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [280259481600, 143731, 482630400, 88695272904, 193999420531], 'label': '77760.bo.720.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.s1', 'old_label': '720.ey1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ey1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246055085
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.el1', '240.cg1', '240.ch1', '360.f1', '360.bl1', '360.ca1'], 'contains': ['1440.bk1', '1440.ce1', '1440.cs1', '2160.fp1', '2160.fq1', '2160.fr1', '2160.fs1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [442641300629, 143975, 997965813, 519235320, 80787], 'label': '77760.bo.720.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '720.ez1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ez1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246055086
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.cg1', '360.cb1'], 'contains': ['1440.bl1', '1440.cj1', '1440.cv1', '2160.fp1', '2160.fu1', '2160.fv1', '2160.fy1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [456053069398, 93448938480, 148, 180587272349, 174400128148], 'label': '77760.bo.720.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.cb1', 'old_label': '720.fa1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.fa1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246055087
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.cg1', '360.a1', '360.p1', '360.cc1'], 'contains': ['1440.bm1', '1440.ck1', '1440.cw1', '2160.fp1', '2160.ft1', '2160.fw1', '2160.fx1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [93448857748, 456053069398, 148, 180587272349, 174400128148], 'label': '77760.bo.720.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '720.fb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.fb1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246055088
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.em1', '240.cg1', '240.ck1', '360.h1', '360.bl1', '360.bz1'], 'contains': ['1440.bn1', '1440.bz1', '1440.cs1', '2160.fq1', '2160.ft1', '2160.fu1', '2160.gd1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [518964004, 997961035, 80880, 80787, 442641024450], 'label': '77760.bo.720.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '720.fc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.fc1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246055089
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.cg1', '240.ci1', '360.i1'], 'contains': ['1440.bt1', '1440.cb1', '1440.ct1', '2160.fs1', '2160.fw1', '2160.fy1', '2160.gd1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [93449036612, 83543730, 174400307012, 180587415845, 80787], 'label': '77760.bo.720.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.i1', 'old_label': '720.fd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.fd1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246055090
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.cg1', '240.cj1', '360.j1', '360.q1', '360.bu1'], 'contains': ['1440.bu1', '1440.cd1', '1440.cu1', '2160.fr1', '2160.fv1', '2160.fx1', '2160.gd1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [174400208787, 93448938387, 456053150130, 180587272349, 80787], 'label': '77760.bo.720.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.r1', 'old_label': '720.fe1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.fe1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246055091
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.eo1', '240.ch1', '240.cj1', '360.n1', '360.z1', '360.ca1'], 'contains': ['1440.bo1', '1440.ce1', '1440.cn1', '2160.fr1', '2160.fz1', '2160.ge1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [518964004, 997965813, 442641109705, 80880, 80787], 'label': '77760.bo.720.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '720.ff1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ff1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246055092
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.ep1', '240.ch1', '240.ci1', '360.ba1'], 'contains': ['1440.bq1', '1440.cf1', '1440.co1', '2160.fs1', '2160.ge1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [997965813, 519235320, 442641109705, 80880, 80787], 'label': '77760.bo.720.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ba1', 'old_label': '720.fg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.fg1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055093
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.ch1', '240.ck1', '360.bb1', '360.bf1', '360.co1', '360.cx1', '360.cx2', '360.dz1', '360.dz2'], 'contains': ['1440.br1', '1440.cg1', '1440.cp1', '2160.fq1', '2160.ge1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [87182277597, 143975, 375138270474, 80880, 80787], 'label': '77760.bo.720.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.x1', 'old_label': '720.fh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.fh1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055094
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '40.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['20.a1', '20.c1', '20.f1'], 'contains': ['80.m1', '80.n1', '80.q1', '120.bv1', '120.bx1', '360.ea1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [180587277504, 93449001331, 83467916, 143975, 174400173363, 456053150130, 80880, 80787], 'label': '77760.bo.40.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.p1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246055095
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.fh2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.bb2', '360.bf2', '360.co2', '360.cx1', '360.cx3', '360.dz1', '360.dz2'], 'contains': ['1440.br1', '1440.cg1', '1440.cp1', '2160.fq2', '2160.ge2'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [448908278999, 442641300482, 143975, 80880, 80787], 'label': '77760.bo.720.fh2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '720.fh2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.fh2', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055096
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.cj1', '360.cb1'], 'contains': ['1440.bw1', '1440.cj1', '1440.cq1', '2160.fv1', '2160.fz1', '2160.gg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [93449036612, 456053069398, 174400128000, 224515, 180587272349], 'label': '77760.bo.720.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.cb1', 'old_label': '720.fi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.fi1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246055097
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.cj1', '360.c1', '360.g1', '360.cc1'], 'contains': ['1440.bx1', '1440.ck1', '1440.cr1', '2160.fx1', '2160.fz1', '2160.gf1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [93449082115, 456053069398, 174400128000, 224515, 180587272349], 'label': '77760.bo.720.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '720.fj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.fj1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246055098
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.cm1', '360.a1', '360.g1', '360.ck1'], 'contains': ['1440.bm1', '1440.bx1', '1440.dg1', '2160.ga1', '2160.gb1', '2160.gc1', '2160.gh1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [180587456184, 93449082115, 456053207518, 174400128000, 224515], 'label': '77760.bo.720.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '720.fk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.fk1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246055099
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.es1', '240.cm1', '240.cn1', '360.h1', '360.z1', '360.ch1'], 'contains': ['1440.bn1', '1440.bo1', '1440.cx1', '2160.ga1', '2160.gi1', '2160.gj1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [518964004, 997961035, 442641109705, 80880, 80787], 'label': '77760.bo.720.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '720.fl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.fl1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246055100
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.et1', '240.cl1', '240.cn1', '360.ba1'], 'contains': ['1440.bp1', '1440.bq1', '1440.cy1', '2160.gi1', '2160.gk1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [368871287518, 143975, 174436416243, 375138172555, 80787], 'label': '77760.bo.720.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ba1', 'old_label': '720.fm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.fm1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055101
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.cn1', '360.bb1', '360.cq1', '360.cx2', '360.cx3', '360.ei1'], 'contains': ['1440.br1', '1440.cz1', '2160.gi1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [442641300482, 143975, 443120071554, 80880, 80787], 'label': '77760.bo.720.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.x1', 'old_label': '720.fn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.fn1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055103
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['240.cl1', '240.cm1', '360.i1'], 'contains': ['1440.bs1', '1440.bt1', '1440.dc1', '2160.gb1', '2160.gj1', '2160.gk1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [180587456184, 93448938387, 456053073961, 174400128243, 80787], 'label': '77760.bo.720.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.i1', 'old_label': '720.fo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.fo1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246055104
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.cm1', '360.j1', '360.bw1'], 'contains': ['1440.bu1', '1440.de1', '2160.gc1', '2160.gj1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [180587456184, 174400208787, 93448938387, 456053073961, 80787], 'label': '77760.bo.720.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.r1', 'old_label': '720.fp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.fp1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246055105
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '40.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.d1', '20.b1', '20.c1', '20.h1'], 'contains': ['80.m1', '80.o1', '120.bw1', '120.bz1', '360.ej1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [180587277504, 83601118, 456053207518, 93449001331, 143975, 174400173363, 80880, 80787], 'label': '77760.bo.40.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.q1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246055106
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.cl1'], 'contains': ['1440.bv1', '1440.df2', '2160.gk1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [180587456184, 93449036612, 174400173363, 456053073961, 80787], 'label': '77760.bo.720.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '720.fq1', 'old_label': '720.fq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.fq1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055107
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.er1', '240.ci1', '240.cj1', '240.ck1', '360.n1', '360.bd1', '360.bz1'], 'contains': ['1440.by1', '1440.bz1', '1440.cn1', '2160.gd1', '2160.ge1', '2160.gf1', '2160.gg1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [368871153961, 375138087093, 174436416243, 80880, 80787], 'label': '77760.bo.720.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '720.fr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.fr1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246055108
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.ev1', '240.cl1', '240.cm1', '240.cn1', '360.f1', '360.bd1', '360.ch1'], 'contains': ['1440.bk1', '1440.by1', '1440.cx1', '2160.gh1', '2160.gi1', '2160.gj1', '2160.gk1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [997925759, 442641300482, 143975, 519235320, 80787], 'label': '77760.bo.720.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '720.fs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.fs1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246055109
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '720.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.bk1', '360.cr1', '360.cx1', '360.cx2', '360.cx3'], 'contains': ['1440.cp1', '1440.cz1', '2160.gl1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 268244748747, 274468002505, 80880, 80787], 'label': '77760.bo.720.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.x1', 'old_label': '720.ft1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ft1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055110
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.f1', '405.b1'], 'contains': ['1620.a1', '1620.e1', '1620.n1', '1620.o1', '1620.p1', '1620.ev1', '1620.fd1', '1620.ff1', '1620.gl1', '1620.gq1', '1620.gx1', '2430.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [461841090505, 357597, 45363, 448908001949, 462320363997, 19679027763], 'label': '77760.bo.810.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '810.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055111
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['270.b1', '270.g1', '405.b1'], 'contains': ['1620.d1', '1620.e2', '1620.f1', '1620.l1', '1620.n1', '1620.u1', '1620.v1', '1620.eu1', '1620.ew1', '1620.fj1', '1620.fl1', '1620.gp1', '1620.gr1', '1620.gz1', '1620.hm1', '2430.b1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [357597, 45363, 461841281758, 448908283914, 19679027763, 462320011466], 'label': '77760.bo.810.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '810.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055112
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.h1', '405.b1'], 'contains': ['1620.c1', '1620.e2', '1620.g1', '1620.m1', '1620.p1', '1620.ep1', '1620.ey1', '1620.fp1', '1620.fr1', '1620.gm1', '1620.gs1', '2430.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [461841090505, 357597, 45363, 448908283914, 19679027763, 462320011466], 'label': '77760.bo.810.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '810.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055113
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['270.a1', '270.j1', '405.b1'], 'contains': ['1620.b1', '1620.c1', '1620.d1', '1620.e1', '1620.h1', '1620.r1', '1620.v1', '1620.eo1', '1620.eq1', '1620.ex1', '1620.ez1', '1620.fv1', '1620.ga1', '1620.ha1', '1620.hh1', '2430.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841090505, 357597, 45363, 462320363997, 448908283914, 19679027763], 'label': '77760.bo.810.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '810.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.d1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055114
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['270.a1', '270.i1', '270.k1', '405.a1'], 'contains': ['1620.i1', '1620.s1', '1620.w1', '1620.fw1', '1620.gc1', '1620.hb1', '1620.hi1', '2430.d1', '3240.b1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [355462951825, 87661140625, 462320225425, 219025, 482635561, 375138305425], 'label': '77760.bo.810.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '810.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.e1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055115
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['270.a1', '270.l1'], 'contains': ['1620.j1', '1620.t1', '1620.x1', '1620.fy1', '1620.gd1', '1620.hc1', '1620.hj1', '2430.d1', '3240.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [19678982400, 462320011709, 5309, 448908284158, 461841010109, 262496684612], 'label': '77760.bo.810.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.f1', 'old_label': '810.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.f1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055116
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '40.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['20.a1', '20.h1'], 'contains': ['80.m1', '80.p1', '120.by1', '360.ek1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [180587277504, 83601118, 456053074316, 93449001331, 143975, 174400173363, 80880, 80787], 'label': '77760.bo.40.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.r1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246055117
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['270.b1', '270.m1', '270.n1', '405.a1'], 'contains': ['1620.k1', '1620.q1', '1620.w1', '1620.gf1', '1620.gg1', '1620.he1', '1620.hi1', '2430.b1', '3240.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [355462951825, 375138091561, 462320011561, 87660926761, 219025, 482635561], 'label': '77760.bo.810.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '810.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.g1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055118
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.d2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.c1', '270.o1', '405.b1'], 'contains': ['1620.a1', '1620.f1', '1620.g1', '1620.h1', '1620.y1', '1620.er1', '1620.fh1', '1620.fn1', '1620.ft1', '1620.gi1', '1620.ho1', '2430.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [357597, 45363, 462320363997, 461841281758, 448908283914, 19679027763], 'label': '77760.bo.810.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '810.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.h1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246055119
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['54.a1', '270.c1', '270.p1', '270.q1', '405.a1'], 'contains': ['1620.i1', '1620.k1', '1620.z1', '1620.fw1', '1620.gf1', '1620.gk1', '1620.hu1', '2430.e1', '3240.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [40349, 19678982400, 448908001949, 262496505600, 461841045149, 462320046749], 'label': '77760.bo.810.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '810.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.i1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055120
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.d1', '270.r1', '405.b1'], 'contains': ['1620.m1', '1620.o1', '1620.r1', '1620.u1', '1620.y1', '1620.go1', '1620.gw1', '1620.hg1', '1620.hl1', '1620.hq1', '1620.hs1', '2430.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [179012, 19678982400, 5309, 448908284158, 461841010109, 462320328958], 'label': '77760.bo.810.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '810.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.j1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055155
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.bl1', '270.bu1'], 'contains': ['1620.db1', '1620.dl1', '1620.dp1', '1620.fx1', '1620.hf1', '2430.o1', '3240.br1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841004800, 362615, 262496787716, 19678982400, 448908284158, 462320006400], 'label': '77760.bo.810.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bp1', 'old_label': '810.bp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.bp1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055121
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['54.b1', '270.d1', '270.s1', '270.t1', '405.a1'], 'contains': ['1620.q1', '1620.s1', '1620.z1', '1620.hb1', '1620.he1', '1620.hu1', '1620.hv1', '2430.f1', '3240.m1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [183845, 461841188645, 19678982400, 448908001949, 262496505600, 462320046749], 'label': '77760.bo.810.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '810.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.k1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055122
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.u1', '270.x1', '405.a1'], 'contains': ['1620.i1', '1620.q1', '1620.bb1', '1620.da1', '1620.di1', '2430.j1', '3240.q1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [461841045385, 262496506293, 19678982400, 40585, 462320046985, 693], 'label': '77760.bo.810.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '810.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.l1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055123
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['162.a1', '270.v1', '270.y1', '405.a1'], 'contains': ['1620.k1', '1620.s1', '1620.bb1', '1620.dc1', '1620.dk1', '2430.h1', '3240.r1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [188331234504, 87182103845, 482814245, 85805, 375138172205, 143304], 'label': '77760.bo.810.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '810.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.m1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055124
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.c1', '270.w1', '270.z1', '405.a1'], 'contains': ['1620.w1', '1620.z1', '1620.bb1', '1620.do1', '1620.dr1', '2430.k1', '3240.s1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [87182277597, 262972235997, 355938191305, 317252, 374659442397, 85705], 'label': '77760.bo.810.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '810.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.n1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055125
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.ba1', '405.b1'], 'contains': ['1620.be1', '1620.bj1', '1620.bu1', '1620.bv1', '1620.ca1', '1620.eo1', '1620.er1', '1620.ff1', '1620.go1', '1620.gp1', '1620.gs1', '2430.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [461841281758, 462320011466, 45363, 448908283914, 5066, 19679027763], 'label': '77760.bo.810.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '810.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.o1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055126
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.f1', '270.ba1', '405.c1'], 'contains': ['1620.bc1', '1620.bl1', '1620.by1', '1620.bz1', '1620.cb1', '1620.es1', '1620.fb1', '1620.fe1', '1620.gn1', '1620.gt1', '1620.gy1', '2430.a1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [461841327358, 19679028004, 448908284158, 85805, 80787, 462320046985], 'label': '77760.bo.810.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '810.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.p1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055127
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '40.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '20.c1', '20.g1'], 'contains': ['80.n1', '80.o1', '120.ca1', '120.cb1', '360.eq1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 10, 'diagramx': None, 'generators': [180587277504, 93449001331, 83543730, 143975, 174400173363, 456053150130, 80880, 80787], 'label': '77760.bo.40.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.s1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246055128
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['270.m1', '270.bb1', '405.b1'], 'contains': ['1620.bi1', '1620.bj2', '1620.bn1', '1620.bs1', '1620.bu1', '1620.cd1', '1620.cg1', '1620.ep1', '1620.eq1', '1620.fh1', '1620.fl1', '1620.gq1', '1620.gr1', '1620.hg1', '1620.hh1', '2430.b1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841090505, 45363, 448908001949, 462320363997, 5066, 19679027763], 'label': '77760.bo.810.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '810.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.q1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055129
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['270.g1', '270.n1', '270.bb1', '405.c1'], 'contains': ['1620.bk1', '1620.bl2', '1620.bm1', '1620.bw1', '1620.by1', '1620.cf1', '1620.ch1', '1620.es2', '1620.et1', '1620.fi1', '1620.fk1', '1620.gt1', '1620.gu1', '1620.hd1', '1620.hn1', '2430.b1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [277050, 461841327358, 19679028004, 448908284158, 80787, 462320046985], 'label': '77760.bo.810.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '810.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.r1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055130
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.bc1', '405.b1'], 'contains': ['1620.bg1', '1620.bj2', '1620.bp1', '1620.bt1', '1620.ca1', '1620.eu1', '1620.ex1', '1620.fn1', '1620.fr1', '1620.gw1', '1620.gx1', '2430.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [183845, 179012, 19678982400, 448908284158, 461841010109, 462320328485], 'label': '77760.bo.810.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '810.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.s1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055131
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.h1', '270.bc1', '405.c1'], 'contains': ['1620.bh1', '1620.bl2', '1620.bo1', '1620.bx1', '1620.cb1', '1620.es2', '1620.fa1', '1620.fo1', '1620.fq1', '1620.gv1', '1620.gy1', '2430.c1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [461841090505, 277050, 19679028004, 448908284158, 462320046842, 80787], 'label': '77760.bo.810.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '810.t1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.t1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055132
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['270.i1', '270.bd1', '405.b1'], 'contains': ['1620.bf1', '1620.bg1', '1620.bi1', '1620.bj1', '1620.br1', '1620.cc1', '1620.cg1', '1620.ev1', '1620.ew1', '1620.ey1', '1620.ez1', '1620.ft1', '1620.ga1', '1620.hl1', '1620.hm1', '2430.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [19679063280, 462320092205, 448908001949, 85805, 461841143189, 80880], 'label': '77760.bo.810.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '810.u1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.u1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055133
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['270.j1', '270.k1', '270.l1', '270.bd1', '405.c1'], 'contains': ['1620.bd1', '1620.bh1', '1620.bk1', '1620.bl1', '1620.bq1', '1620.ce1', '1620.ch1', '1620.es1', '1620.et1', '1620.fa1', '1620.fc1', '1620.fu1', '1620.fz1', '1620.hk1', '1620.hn1', '2430.d1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841223825, 183845, 462320225425, 19679028004, 448908001949, 80787], 'label': '77760.bo.810.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '810.v1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.v1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055134
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.cg2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.o1', '270.p1', '270.be1', '405.c1'], 'contains': ['1620.bc1', '1620.bm1', '1620.bo1', '1620.bq1', '1620.ci1', '1620.fb1', '1620.fi1', '1620.fo1', '1620.fu1', '1620.gh1', '1620.hp1', '2430.e1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [461841009961, 40349, 19679028004, 448908001949, 80787, 462320046749], 'label': '77760.bo.810.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '810.w1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.w1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055135
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.q1', '270.be1', '405.b1'], 'contains': ['1620.be1', '1620.bn1', '1620.bp1', '1620.br1', '1620.cj1', '1620.fd1', '1620.fj1', '1620.fp1', '1620.fv1', '1620.gi1', '1620.hq1', '2430.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [461841223825, 219025, 19678982400, 143975, 448908284158, 462320328958], 'label': '77760.bo.810.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '810.x1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.x1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055136
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.s1', '270.bf1', '405.b1'], 'contains': ['1620.bt1', '1620.bv1', '1620.cc1', '1620.cd1', '1620.cj1', '1620.gl1', '1620.gm1', '1620.gz1', '1620.ha1', '1620.ho1', '1620.hs1', '2430.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [461841090505, 45363, 462320363997, 5066, 448908283914, 19679027763], 'label': '77760.bo.810.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '810.y1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.y1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055137
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.r1', '270.t1', '270.bf1', '405.c1'], 'contains': ['1620.bx1', '1620.bz1', '1620.ce1', '1620.cf1', '1620.ci1', '1620.gn1', '1620.gv1', '1620.hd1', '1620.hk1', '1620.hp1', '1620.hr1', '2430.f1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [461841090505, 19679028004, 5309, 448908284158, 462320328958, 80787], 'label': '77760.bo.810.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '810.z1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.z1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055138
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '45.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3.a1', '15.a1'], 'contains': ['90.a1', '90.b1', '90.c1', '90.d1', '90.j1', '90.m1', '90.o1', '90.q1', '90.r1', '90.s1', '90.t1', '90.z1', '90.ba1', '90.bb1', '90.bd1', '135.a1', '135.b1', '135.c1', '180.bt1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 80787, 262496586694, 143304, 448908284158, 85805, 19679028004, 461841045385, 462320328386], 'label': '77760.bo.45.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '45.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '45.a1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246055139
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.bg1', '405.b1'], 'contains': ['1620.a1', '1620.b1', '1620.l1', '1620.m1', '1620.be1', '1620.bf1', '1620.bs1', '1620.bt1', '1620.ck2', '1620.cl1', '1620.cm1', '1620.dv1', '1620.dw1', '1620.ef1', '1620.eg1', '2430.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [7185207845, 462320283121, 19678982400, 143975, 85805, 143304], 'label': '77760.bo.810.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '810.ba1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.ba1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055140
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['270.v1', '270.bh1', '405.b1'], 'contains': ['1620.c1', '1620.f1', '1620.n1', '1620.r1', '1620.bg1', '1620.bn1', '1620.bu1', '1620.cc1', '1620.ck1', '1620.cl1', '1620.cn1', '1620.du1', '1620.dy1', '1620.ee1', '1620.ej1', '2430.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [442641104880, 443120025600, 180667249346, 5066, 80880, 143304], 'label': '77760.bo.810.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '810.bb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.bb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055141
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.e1', '270.bi1', '405.b1'], 'contains': ['1620.d1', '1620.g1', '1620.o1', '1620.bi1', '1620.bp1', '1620.bv1', '1620.ck1', '1620.cm1', '1620.dt1', '1620.ea1', '1620.eh1', '2430.i1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [87261753748, 456053074316, 83462998, 5066, 148, 693], 'label': '77760.bo.810.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '810.bc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.bc1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055142
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['270.u1', '270.bj1', '405.b1'], 'contains': ['1620.e1', '1620.e2', '1620.h1', '1620.u1', '1620.bj1', '1620.bj2', '1620.br1', '1620.cd1', '1620.ck1', '1620.ck2', '1620.cn1', '1620.ds1', '1620.ds2', '1620.ec1', '1620.ek1', '2430.j1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [19678982400, 143975, 40585, 448908284158, 462320328386, 143304], 'label': '77760.bo.810.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '810.bd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.bd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055143
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.w1', '270.bk1', '405.b1'], 'contains': ['1620.p1', '1620.v1', '1620.y1', '1620.ca1', '1620.cg1', '1620.cj1', '1620.cm1', '1620.cn1', '1620.ei1', '1620.el1', '1620.em1', '2430.k1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [374659361758, 87182277597, 362615, 45363, 355938191305, 5066], 'label': '77760.bo.810.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '810.be1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.be1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055144
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.y1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['270.bg1', '405.c1'], 'contains': ['1620.bc1', '1620.bd1', '1620.bw1', '1620.bx1', '1620.co2', '1620.cp1', '1620.cq1', '1620.cv1', '1620.cw1', '1620.de1', '1620.df1', '2430.g1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [7185207845, 19679028004, 85805, 80787, 462320046985, 143304], 'label': '77760.bo.810.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '810.bf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.bf1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055145
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.y1', '270.bh1', '405.c1'], 'contains': ['1620.bh1', '1620.bm1', '1620.by1', '1620.ce1', '1620.co1', '1620.cp1', '1620.cr1', '1620.cu1', '1620.cx1', '1620.dd1', '1620.dj1', '2430.h1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [80787, 85805, 375138172205, 362615, 482952958, 87182277597], 'label': '77760.bo.810.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '810.bg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.bg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055146
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.f1', '270.bi1', '405.c1'], 'contains': ['1620.bk1', '1620.bo1', '1620.bz1', '1620.co1', '1620.cq1', '1620.ct1', '1620.cy1', '1620.dg1', '2430.i1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [40349, 83543730, 456053154955, 87261834387, 45813, 80787], 'label': '77760.bo.810.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '810.bh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.bh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055147
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.x1', '270.bj1', '405.c1'], 'contains': ['1620.bl1', '1620.bl2', '1620.bq1', '1620.cf1', '1620.co1', '1620.co2', '1620.cr1', '1620.cs1', '1620.cs2', '1620.cz1', '1620.dm1', '2430.j1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [461841090505, 178680, 19679028004, 5309, 462320046842, 80787], 'label': '77760.bo.810.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '810.bi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.bi1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055148
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['270.z1', '270.bk1', '405.c1'], 'contains': ['1620.cb1', '1620.ch1', '1620.ci1', '1620.cq1', '1620.cr1', '1620.dh1', '1620.dn1', '1620.dq1', '2430.k1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [87182277597, 282215, 5309, 374659361850, 355938110909, 80787], 'label': '77760.bo.810.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '810.bj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.bj1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055149
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '45.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1'], 'contains': ['90.g1', '90.h1', '90.i1', '90.l1', '90.n1', '90.p1', '90.u1', '90.v1', '90.w1', '90.x1', '90.y1', '90.be1', '90.bf1', '90.bg1', '90.bh1', '90.bi1', '90.bj1', '135.c1'], 'core': '720.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [461841090505, 143975, 80787, 143304, 85805, 19678982548, 448908283914, 80880, 462320328386], 'label': '77760.bo.45.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '45.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '45.b1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246055150
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['270.bp1', '405.c1'], 'contains': ['1620.cs1', '1620.cv1', '1620.dd1', '1620.dg1', '1620.dh1', '1620.fb1', '1620.fc1', '1620.gu1', '1620.gv1', '2430.l1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [282215, 461841090505, 19679028004, 462320052004, 448908284158, 80787], 'label': '77760.bo.810.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '810.bk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.bk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055151
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.bm1', '270.bq1', '405.c1'], 'contains': ['1620.cs2', '1620.ct1', '1620.cx1', '1620.dd1', '1620.de1', '1620.dm1', '1620.dn1', '1620.fa1', '1620.fi1', '1620.gt1', '1620.hk1', '2430.m1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [282215, 461841090505, 19679028004, 448908284158, 462320046842, 80787], 'label': '77760.bo.810.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '810.bl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.bl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055152
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['270.br1', '405.c1'], 'contains': ['1620.cs2', '1620.cu1', '1620.cy1', '1620.df1', '1620.dh1', '1620.et1', '1620.fo1', '1620.gn1', '2430.n1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [317399, 448908278999, 461841009961, 19679028004, 80787, 462320046749], 'label': '77760.bo.810.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '810.bm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.bm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055153
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.bl1', '270.bs1', '405.c1'], 'contains': ['1620.cs1', '1620.ct1', '1620.cu1', '1620.cw1', '1620.cz1', '1620.dj1', '1620.dn1', '1620.es1', '1620.es2', '1620.fu1', '1620.hd1', '2430.o1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [362615, 19679028004, 462320052004, 448908284158, 461841050404, 80787], 'label': '77760.bo.810.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '810.bn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.bn1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055154
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.bl1', '270.bt1', '405.a1'], 'contains': ['1620.da1', '1620.dk1', '1620.do1', '1620.fw1', '1620.he1', '2430.o1', '3240.bq1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [262496868215, 461841004800, 362615, 19678982400, 448908284158, 462320006400], 'label': '77760.bo.810.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '810.bo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.bo1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055156
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.bm1', '270.bv1', '405.a1'], 'contains': ['1620.dc1', '1620.di1', '1620.do1', '1620.gf1', '1620.hb1', '2430.m1', '3240.bt1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [461841004800, 281971, 19678982400, 262496787571, 448908243571, 462320046749], 'label': '77760.bo.810.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '810.bq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.bq1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055157
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bs2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['270.bn1', '270.bw1', '270.bx1', '405.c1'], 'contains': ['1620.cv1', '1620.cx1', '1620.cy1', '1620.cz1', '1620.dq1', '1620.fe1', '1620.fk1', '1620.fq1', '1620.fz1', '1620.gh1', '1620.hr1', '2430.p1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [317399, 448908278999, 19679028004, 462320052004, 461841050404, 80787], 'label': '77760.bo.810.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '810.br1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.br1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246055158
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.f1', '270.bn1', '270.by1', '270.bz1', '405.a1'], 'contains': ['1620.da1', '1620.dc1', '1620.dr1', '1620.gc1', '1620.gg1', '1620.gk1', '1620.hv1', '2430.p1', '3240.bu1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [461841004800, 281971, 19678982400, 262496787571, 448908243571, 462320006400], 'label': '77760.bo.810.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '810.bs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.bs1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055159
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['270.bo1', '270.ca1', '405.c1'], 'contains': ['1620.df1', '1620.dg1', '1620.dj1', '1620.dm1', '1620.dq1', '1620.gy1', '1620.hn1', '1620.hp1', '2430.q1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [362615, 19679028004, 448908284158, 461841050404, 80787, 462320046985], 'label': '77760.bo.810.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '810.bt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.bt1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055160
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '48.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '24.b1', '24.c1', '24.d1', '24.e1', '24.f1'], 'contains': ['144.i1', '144.j1', '240.bv1', '288.c1', '480.n1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [286483098115, 143975, 80880, 80787, 25470771715], 'label': '77760.bo.48.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1', 'subgroup_fusion': None, 'weyl_group': '4320.bp'}
  • id: 246055161
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.g1', '270.bo1', '270.cb1', '405.a1'], 'contains': ['1620.di1', '1620.dk1', '1620.dr1', '1620.hi1', '1620.hu1', '2430.q1', '3240.cb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [482854584, 224184, 375138126749, 87661105445, 355462956984, 462320046749], 'label': '77760.bo.810.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '810.bu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.bu1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055162
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.bp1', '405.b1'], 'contains': ['1620.ds1', '1620.dv1', '1620.ee1', '1620.eh1', '1620.ei1', '1620.er1', '1620.ez1', '1620.fd1', '1620.gm1', '1620.gr1', '1620.gw1', '2430.l1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [362615, 461841090505, 45363, 462320006400, 448908283914, 19679027763], 'label': '77760.bo.810.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '810.bv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.bv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055163
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['270.bq1', '270.bv1', '405.b1'], 'contains': ['1620.ds2', '1620.dt1', '1620.dy1', '1620.ee1', '1620.ef1', '1620.ek1', '1620.el1', '1620.ex1', '1620.ey1', '1620.fh1', '1620.fj1', '1620.gp1', '1620.gq1', '1620.ha1', '1620.hl1', '2430.m1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [362615, 461841090505, 45363, 448908283914, 19679027763, 462320011466], 'label': '77760.bo.810.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '810.bw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.bw1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055164
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.br1', '405.b1'], 'contains': ['1620.ds2', '1620.du1', '1620.ea1', '1620.eg1', '1620.ei1', '1620.eq1', '1620.ew1', '1620.fn1', '1620.fp1', '1620.gl1', '1620.go1', '2430.n1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [461841009961, 462320283029, 224184, 19678982400, 224515, 448908243571], 'label': '77760.bo.810.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '810.bx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.bx1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055165
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['270.bs1', '270.bt1', '270.bu1', '405.b1'], 'contains': ['1620.ds1', '1620.dt1', '1620.du1', '1620.dw1', '1620.ec1', '1620.ej1', '1620.el1', '1620.eo1', '1620.ep1', '1620.eu1', '1620.ev1', '1620.ft1', '1620.fv1', '1620.gz1', '1620.hg1', '2430.o1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841050163, 362615, 45363, 462320006400, 448908283914, 19679027763], 'label': '77760.bo.810.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '810.by1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.by1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055166
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.v2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.bw1', '270.by1', '405.b1'], 'contains': ['1620.dv1', '1620.dy1', '1620.ea1', '1620.ec1', '1620.em1', '1620.ff1', '1620.fl1', '1620.fr1', '1620.ga1', '1620.gi1', '1620.hs1', '2430.p1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [461841050163, 362615, 45363, 448908243571, 462320006400, 19679027763], 'label': '77760.bo.810.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '810.bz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.bz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055167
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['270.bx1', '270.bz1'], 'contains': ['1620.dx1', '1620.dz1', '1620.eb1', '1620.ed1', '1620.en1', '1620.fg1', '1620.fm1', '1620.fs1', '1620.gb1', '1620.gj1', '1620.ht1', '2430.p1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [461841004800, 462320287944, 19678982400, 143731, 448908243571, 143304], 'label': '77760.bo.810.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '810.ca1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.ca1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055168
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '810.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.ca1', '270.cb1', '405.b1'], 'contains': ['1620.eg1', '1620.eh1', '1620.ej1', '1620.ek1', '1620.em1', '1620.gs1', '1620.gx1', '1620.hh1', '1620.hm1', '1620.ho1', '1620.hq1', '2430.q1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [462320011466, 362615, 45363, 448908283914, 461841050163, 19679027763], 'label': '77760.bo.810.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '810.cb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.cb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055169
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '864.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.a1', '432.a1', '432.b1', '432.e1'], 'contains': ['1728.a1', '2592.a1', '2592.b1', '4320.e1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [18764743922, 183845, 80880, 80787], 'label': '77760.bo.864.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '864.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.a1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 246055170
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '864.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.a1', '432.c1', '432.d1', '432.e1'], 'contains': ['1728.a1', '2592.b1', '2592.c1', '4320.a1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [85805, 80880, 80787, 18764565242], 'label': '77760.bo.864.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '864.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.b1', 'subgroup_fusion': None, 'weyl_group': '432.300'}
  • id: 246055171
    {'ambient': '77760.bo', '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': '77760.a1', 'complements': ['12960.i1', '12960.j1', '12960.e1', '12960.bt1', '12960.bu1', '12960.bo1', '12960.bw1', '12960.bx1', '12960.br1', '12960.bh1', '12960.bi1', '12960.ba1', '12960.bk1', '12960.bl1', '12960.bd1'], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.a1', '12.b1', '12.c1', '18.c1', '18.d1', '36.g1', '60.g1', '90.o1'], 'core': '6.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [183845, 143975, 462320328958, 93924236159, 80787], 'label': '77760.bo.6.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['12.a1', '12.b1', '12.c1'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '77760.bo', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '77760.bo'}
  • id: 246055172
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.a1', '18.c1', '18.d1', '27.a1'], 'contains': ['108.a1', '108.d1', '108.r1', '324.a1', '540.d1', '810.i1'], 'core': '108.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93924235466, 5066, 462320011466], 'label': '77760.bo.54.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1', 'subgroup_fusion': None, 'weyl_group': '720.763'}
  • id: 246055173
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '864.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.b1', '432.e1', '432.f1', '432.h1'], 'contains': ['1728.a1', '2592.d1', '2592.e1', '4320.l1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [18764748747, 178680, 143975, 80787], 'label': '77760.bo.864.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '864.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.c1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 246055174
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '864.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.b1', '432.g1'], 'contains': ['1728.b1', '2592.d1', '2592.f1', '4320.m1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [18764748747, 178680, 80787, 179159], 'label': '77760.bo.864.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.m1', 'old_label': '864.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.d1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 246055175
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '864.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.i1', '288.c1', '432.a1', '432.c1', '432.f1', '432.i1', '432.j1', '432.k1', '432.l1'], 'contains': ['1728.a1', '2592.g1', '2592.h1', '4320.bh1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1037836800, 18764570163, 80880, 80787], 'label': '77760.bo.864.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '864.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.e1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 246055176
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '864.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.j1', '288.c1', '432.g1', '432.m1', '432.n1'], 'contains': ['1728.b1', '2592.g1', '2592.i1', '4320.bi1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1037836800, 18764605587, 80787, 179159], 'label': '77760.bo.864.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '864.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.f1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246055177
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '864.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.d1', '432.a1', '432.d1', '432.h1'], 'contains': ['1728.a1', '2592.j1', '2592.k1', '4320.cw1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1038020645, 18764570163, 80880, 80787], 'label': '77760.bo.864.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '864.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.g1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 246055178
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '864.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.d1', '432.b1', '432.c1', '432.h1'], 'contains': ['1728.a1', '2592.k1', '2592.l1', '4320.cz1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [143975, 1038020645, 18764605587, 80787], 'label': '77760.bo.864.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '864.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.h1', 'subgroup_fusion': None, 'weyl_group': '2160.cr'}
  • id: 246055179
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '864.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.e1', '432.b1', '432.d1', '432.f1'], 'contains': ['1728.a1', '2592.m1', '2592.n1', '4320.di1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1037980104, 143975, 18764605587, 80787], 'label': '77760.bo.864.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '864.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.i1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 246055180
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '864.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.e1', '432.g1'], 'contains': ['1728.b1', '2592.m1', '2592.o1', '4320.dj1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1037980104, 18764605587, 80787, 179159], 'label': '77760.bo.864.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.m1', 'old_label': '864.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.j1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246055181
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '960.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['320.a1', '480.b1', '480.i1', '480.q1', '480.t1', '480.w1', '480.bc1', '480.bg1'], 'contains': ['2880.b1', '2880.c1', '2880.f1', '2880.g1', '2880.i1', '2880.i2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 160, 'diagramx': None, 'generators': [280259705975, 193999455812, 80880, 80787], 'label': '77760.bo.960.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.a1', 'old_label': '960.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '960.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055182
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '960.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '960.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['320.a1', '480.a1', '480.c1', '480.e1', '480.j1', '480.o1', '480.r1', '480.u1', '480.x1', '480.bd1', '480.bf1', '480.bh1'], 'contains': ['2880.b1', '2880.f1', '2880.h1', '2880.j1', '2880.k1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [280259481600, 143975, 193999455812, 80787], 'label': '77760.bo.960.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '960.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '960.b1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 246055183
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.b1', '18.e1', '18.f1', '27.a1'], 'contains': ['108.d1', '108.r1', '108.s1', '324.b1', '540.h1', '810.k1'], 'core': '216.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [93924235466, 462320363997, 5066], 'label': '77760.bo.54.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1', 'subgroup_fusion': None, 'weyl_group': '720.763'}
  • id: 246055184
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '960.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.bv1', '320.a1', '480.d1', '480.g1', '480.h1', '480.k1', '480.n1', '480.s1', '480.v1', '480.y1', '480.bb1', '480.be1', '480.bi1'], 'contains': ['2880.a1', '2880.b1', '2880.c1', '2880.d1', '2880.e1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [194518374451, 143975, 80880, 80787], 'label': '77760.bo.960.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '960.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '960.c1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055185
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '960.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['320.a1', '480.l1', '480.z1', '480.bj1'], 'contains': ['2880.d1', '2880.e1', '2880.f1', '2880.g1', '2880.i1', '2880.i2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 160, 'diagramx': None, 'generators': [193999455812, 280259527104, 80787, 179159], 'label': '77760.bo.960.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '80.k1', 'old_label': '960.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '960.d1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 246055186
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '960.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '960.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['320.a1', '480.f1', '480.m1', '480.p1', '480.ba1', '480.bk1'], 'contains': ['2880.d1', '2880.g1', '2880.h1', '2880.l1', '2880.m1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [280259481600, 193999420531, 80787, 179159], 'label': '77760.bo.960.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.g1', 'old_label': '960.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '960.e1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 246055187
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '972.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.a1', '324.d1', '324.e1'], 'contains': ['1944.a1', '1944.b1', '1944.c1', '1944.d1', '1944.e1', '4860.s1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [267841814155, 269202614155, 85805, 181146153355, 693], 'label': '77760.bo.972.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.a1', 'old_label': '972.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 246055188
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['270.a1', '360.a1', '360.f1', '540.br1'], 'contains': ['2160.a1', '2160.j1', '2160.k1', '2160.da1', '2160.dh1', '2160.fp1', '2160.gh1', '3240.a1', '3240.b1', '3240.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [219025, 368871153961, 174436554481, 375138305425, 80880], 'label': '77760.bo.1080.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '1080.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055189
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['270.b1', '360.a1', '360.h1', '540.br1'], 'contains': ['2160.b1', '2160.g1', '2160.k1', '2160.dn1', '2160.ds1', '2160.ft1', '2160.ga1', '3240.a1', '3240.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [518918400, 277050, 45363, 998000644, 442641341252], 'label': '77760.bo.1080.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '1080.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055190
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.a1', '360.i1'], 'contains': ['2160.c1', '2160.h1', '2160.l1', '2160.dp1', '2160.du1', '2160.fw1', '2160.gb1', '3240.c1', '3240.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [180587456184, 93449082115, 5161, 174400128000, 456053073961], 'label': '77760.bo.1080.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.c1', 'old_label': '1080.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.c1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055191
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.a1', '360.g1', '360.j1', '540.j1'], 'contains': ['2160.d1', '2160.i1', '2160.m1', '2160.dq1', '2160.dw1', '2160.fx1', '2160.gc1', '3240.b1', '3240.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [180587456184, 219025, 174400128000, 456053073961, 93448857600], 'label': '77760.bo.1080.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.j1', 'old_label': '1080.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.d1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055192
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.b1', '270.c1', '360.b1', '360.k1', '540.br1'], 'contains': ['2160.a1', '2160.b1', '2160.e1', '2160.cv1', '2160.dl1', '2160.dy1', '2160.ev1', '3240.d1', '3240.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [368871287518, 375138225118, 224515, 85946, 174436501946], 'label': '77760.bo.1080.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '1080.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.e1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055193
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.w1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.b1', '360.l1', '360.m1', '540.c1', '540.d1', '540.j1'], 'contains': ['2160.d1', '2160.f1', '2160.dq1', '2160.ea1', '2160.fk1', '3240.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [5161, 174400128000, 456053073961, 180587232000, 93448857600], 'label': '77760.bo.1080.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '1080.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.f1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246055194
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1', '18.h1', '27.a1'], 'contains': ['108.d1', '108.n1', '324.c1', '540.k1', '810.n1'], 'core': '216.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [87182277597, 362615, 274511462400, 5066], 'label': '77760.bo.54.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1', 'subgroup_fusion': None, 'weyl_group': '720.763'}
  • id: 246055195
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.c1', '270.d1', '360.c1', '360.n1', '540.br1'], 'contains': ['2160.e1', '2160.g1', '2160.j1', '2160.ex1', '2160.ez1', '2160.fz1', '2160.gf1', '3240.g1', '3240.m1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [997920598, 86155, 518918400, 148, 442641024450], 'label': '77760.bo.1080.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '1080.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.g1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055196
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.b1', '360.o1', '540.a1', '540.b1', '540.e1', '540.f1', '540.g1', '540.i1', '540.bs1'], 'contains': ['2160.fg1', '3240.n1', '3240.o1', '3240.p1', '4320.b1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [274467916800, 268244524800, 143975, 194518339175, 85805], 'label': '77760.bo.1080.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '1080.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.h1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246055197
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.c1', '360.p1', '360.q1', '540.c1', '540.h1', '540.j1'], 'contains': ['2160.f1', '2160.i1', '2160.fk1', '2160.fl1', '2160.fx1', '3240.m1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [40349, 83462998, 174400128000, 180587232000, 93448857600], 'label': '77760.bo.1080.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.e1', 'old_label': '1080.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.i1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246055198
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.d1', '360.d1', '360.r1', '360.t1', '540.d1', '540.h1', '540.k1'], 'contains': ['2160.f1', '2160.fm1', '2160.fo1', '9720.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [482849425, 219025, 193999276800, 280259700625, 88695348625], 'label': '77760.bo.1080.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '1080.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.j1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246055199
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.e1', '360.s1', '360.u1', '540.c1', '540.k1'], 'contains': ['2160.f1', '2160.fn1', '2160.fo1', '9720.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [5161, 280259486761, 482635561, 193999276800, 88695348625], 'label': '77760.bo.1080.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.e1', 'old_label': '1080.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.k1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246055200
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.v1', '360.x1', '540.j1'], 'contains': ['2160.d1', '2160.i1', '2160.n1', '2160.br1', '2160.bw1', '3240.q1', '3240.r1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [40349, 83462998, 598, 174400128000, 93448857600], 'label': '77760.bo.1080.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.j1', 'old_label': '1080.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.l1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055201
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.w1', '360.y1', '540.j1', '540.k1'], 'contains': ['2160.f1', '2160.m1', '2160.n1', '2160.bt1', '2160.ca1', '3240.s1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [482849425, 40585, 280259522185, 193999420104, 143304], 'label': '77760.bo.1080.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.e1', 'old_label': '1080.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.m1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246055202
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['270.i1', '360.g1', '360.z1', '540.br1'], 'contains': ['2160.r1', '2160.z1', '2160.bd1', '2160.cv1', '2160.dh1', '2160.fz1', '2160.ga1', '3240.b1', '3240.t1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [368871287518, 174436554242, 138242, 224515, 375138172555], 'label': '77760.bo.1080.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '1080.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.n1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055203
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.f1', '360.h1', '360.bb1', '540.p1', '540.p2', '540.cm1'], 'contains': ['2160.o1', '2160.ba1', '2160.be1', '2160.cx1', '2160.dc1', '2160.fq1', '2160.gi1', '3240.a1', '3240.u1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [183845, 87181925066, 375138172205, 80880, 80787], 'label': '77760.bo.1080.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bj1', 'old_label': '1080.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.o1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055204
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.o2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.bb2', '540.p1', '540.p2', '540.cm2'], 'contains': ['2160.o1', '2160.ba1', '2160.be1', '2160.cx2', '2160.dc2', '2160.fq2', '2160.gi2', '3240.a2', '3240.u2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [40349, 442641386852, 448908283441, 143975, 80787], 'label': '77760.bo.1080.o2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.o2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.o2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055205
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['9.a1', '18.i1'], 'contains': ['108.b1', '108.c1', '108.f1', '108.g1', '108.i1', '108.o1', '108.q1', '162.a1', '270.v1', '324.d1', '540.br1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [362615, 174879411571, 45363, 40585, 462320046985], 'label': '77760.bo.54.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '54.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 246055206
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['270.k1', '360.f1', '360.j1', '360.z1', '540.bt1'], 'contains': ['2160.p1', '2160.bb1', '2160.bf1', '2160.cy1', '2160.de1', '2160.fr1', '2160.gj1', '3240.b1', '3240.u1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [518964004, 40349, 442641024000, 997965813, 80787], 'label': '77760.bo.1080.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '1080.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.p1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055207
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['270.l1', '360.f1', '360.i1', '360.ba1'], 'contains': ['2160.q1', '2160.bc1', '2160.bg1', '2160.cz1', '2160.df1', '2160.fs1', '2160.gk1', '3240.c1', '3240.u1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [86155, 442641024000, 997965813, 518963763, 80787], 'label': '77760.bo.1080.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.q1', 'old_label': '1080.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.q1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055208
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.ec1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.k1', '360.bc1', '540.n1', '540.o1', '540.p2', '540.q1', '540.r1', '540.s1', '540.cm1'], 'contains': ['2160.o1', '2160.u1', '2160.cu1', '2160.dj1', '2160.eb1', '3240.d1', '3240.v1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87182277125, 143975, 375138270474, 85805, 80787], 'label': '77760.bo.1080.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.r1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055209
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.r2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.bc2', '540.l1', '540.m1', '540.p1', '540.s1', '540.cm2'], 'contains': ['2160.o1', '2160.u1', '2160.cu2', '2160.dj2', '2160.eb2', '3240.d2', '3240.v2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [442641386187, 40349, 448908283441, 143975, 80787], 'label': '77760.bo.1080.r2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.r2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.r2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055210
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['270.m1', '360.g1', '360.bd1', '540.br1'], 'contains': ['2160.t1', '2160.x1', '2160.bd1', '2160.dl1', '2160.ds1', '2160.gf1', '2160.gh1', '3240.e1', '3240.t1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [183845, 179012, 998099012, 519235320, 442641341252], 'label': '77760.bo.1080.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '1080.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.s1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055211
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['270.n1', '360.h1', '360.i1', '360.j1', '360.bd1', '540.bt1'], 'contains': ['2160.s1', '2160.y1', '2160.bf1', '2160.dm1', '2160.dr1', '2160.gd1', '2160.gj1', '3240.e1', '3240.u1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [518964004, 442641386755, 277050, 998000787, 80787], 'label': '77760.bo.1080.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '1080.t1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.t1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055212
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.e1', '270.p1', '360.k1', '360.l1', '360.be1', '540.bt1'], 'contains': ['2160.p1', '2160.s1', '2160.v1', '2160.cy1', '2160.dm1', '2160.dx1', '2160.ew1', '3240.f1', '3240.v1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [518964004, 183845, 442641024000, 998000787, 80787], 'label': '77760.bo.1080.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '1080.u1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.u1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055213
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.f1', '270.q1', '360.m1', '360.be1', '540.br1'], 'contains': ['2160.r1', '2160.t1', '2160.w1', '2160.da1', '2160.dn1', '2160.dy1', '2160.ex1', '3240.f1', '3240.w1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [997965504, 442641104880, 518918400, 85805, 80880], 'label': '77760.bo.1080.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '1080.v1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.v1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055214
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.n1', '360.bf1', '540.o1', '540.p1', '540.ba1', '540.bb1', '540.bg1', '540.bj1', '540.cm1'], 'contains': ['2160.u1', '2160.ba1', '2160.ec1', '2160.ed1', '2160.ge1', '3240.g1', '3240.y1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87182277125, 143975, 85805, 375138172555, 80787], 'label': '77760.bo.1080.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.w1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.w1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055215
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.w2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.bf2', '540.p2', '540.y1', '540.z1', '540.bj1', '540.cm2'], 'contains': ['2160.u1', '2160.ba1', '2160.ec2', '2160.ed2', '2160.ge2', '3240.g2', '3240.y2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [442641386755, 5309, 143975, 448908284158, 80787], 'label': '77760.bo.1080.w2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.w2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.w2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055216
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.b1', '18.i1'], 'contains': ['108.e1', '108.h1', '108.j1', '108.l1', '108.m1', '162.a1', '270.y1', '324.e1', '540.bt1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [362615, 443555839197, 85805, 479001600, 80787], 'label': '77760.bo.54.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '54.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 246055217
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dp1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.c1', '360.bg1', '540.l1', '540.q1', '540.y1', '540.ba1', '540.cn1'], 'contains': ['2160.u1', '2160.ej1', '2160.eo1', '3240.h1', '3240.z1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [143975, 80787, 267845678885, 443120250115, 5309], 'label': '77760.bo.1080.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.x1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.x1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055218
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dp1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.d1', '360.bh1', '540.l1', '540.r1', '540.z1', '540.bb1', '540.bc1', '540.bo1', '540.co1'], 'contains': ['2160.u1', '2160.ek1', '2160.em1', '3240.i1', '3240.ba1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [88695170185, 143975, 85805, 80787, 482670985], 'label': '77760.bo.1080.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.y1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.y1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055219
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.e1', '360.bi1', '540.m1', '540.o1', '540.y1', '540.bl1', '540.co1'], 'contains': ['2160.u1', '2160.el1', '2160.en1', '3240.j1', '3240.bb1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [40349, 482635561, 143975, 80787, 88695348625], 'label': '77760.bo.1080.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.z1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.z1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055220
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.d1', '360.bj1', '540.m1', '540.n1', '540.z1', '540.bg1', '540.cn1'], 'contains': ['2160.u1', '2160.ep1', '2160.eq1', '3240.k1', '3240.bc1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [267845679358, 443120250115, 143975, 85805, 80787], 'label': '77760.bo.1080.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.ba1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ba1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055221
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.bk1', '540.n1', '540.p1', '540.p2', '540.ba1', '540.bc1', '540.bl1', '540.cp1'], 'contains': ['2160.u1', '2160.be1', '2160.eg1', '2160.eh1', '2160.gl1', '3240.l1', '3240.bi1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [442681124645, 355499159518, 40349, 143975, 80787], 'label': '77760.bo.1080.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.bb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bb1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055222
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.g1', '270.s1', '360.p1', '360.bl1', '540.br1'], 'contains': ['2160.w1', '2160.x1', '2160.z1', '2160.ev1', '2160.ez1', '2160.fp1', '2160.ft1', '3240.m1', '3240.x1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [183845, 997920598, 442641305971, 224515, 519200188], 'label': '77760.bo.1080.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '1080.bc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bc1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055223
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.h1', '270.t1', '360.n1', '360.q1', '360.bl1', '540.bt1'], 'contains': ['2160.v1', '2160.y1', '2160.bb1', '2160.ew1', '2160.ey1', '2160.fr1', '2160.gd1', '3240.m1', '3240.y1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [518964004, 40349, 997965813, 442641024598, 80787], 'label': '77760.bo.1080.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '1080.bd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055224
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.ec1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.o1', '360.bo1', '540.q1', '540.s1', '540.bg1', '540.bj1', '540.bl1', '540.bo1', '540.cp1'], 'contains': ['2160.u1', '2160.ef1', '2160.fb1', '3240.n1', '3240.bj1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [274467962404, 143975, 268244605587, 85805, 80787], 'label': '77760.bo.1080.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '1080.be1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.be1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055225
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.e1', '360.o1', '360.bm1', '540.t1', '540.w1', '540.bf1', '540.bh1', '540.bm1', '540.bp1', '540.bu1'], 'contains': ['2160.fd1', '3240.o1', '3240.bj1', '4320.f1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [355499061242, 442680946109, 5309, 355419232804, 80787], 'label': '77760.bo.1080.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '1080.bf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bf1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246055226
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.o1', '360.bn1', '540.u1', '540.bi1', '540.bn1'], 'contains': ['2160.fe1', '3240.p1', '3240.bj1', '4320.g1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [442681124645, 183845, 355499204645, 355419232563, 80787], 'label': '77760.bo.1080.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1', 'old_label': '1080.bg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bg1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246055227
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.j1', '18.l1', '18.m1', '27.a1'], 'contains': ['108.a1', '108.n1', '108.s1', '324.f1', '540.ct1', '810.bs1'], 'core': '108.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93924231093, 462320006400, 693], 'label': '77760.bo.54.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '54.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.f1', 'subgroup_fusion': None, 'weyl_group': '720.763'}
  • id: 246055228
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.f1', '360.bm1', '540.v1', '540.x1', '540.bd1', '540.be1', '540.bk1', '540.bq1', '540.bs1'], 'contains': ['2160.fg1', '3240.o1', '3240.bk1', '4320.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [274467997680, 268244605680, 85805, 80880, 194518240704], 'label': '77760.bo.1080.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '1080.bh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bh1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246055229
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['270.u1', '360.v1', '360.bp1', '540.br1'], 'contains': ['2160.a1', '2160.g1', '2160.r1', '2160.x1', '2160.bh1', '2160.cd1', '2160.cn1', '3240.q1', '3240.bl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [442641386187, 519280587, 143975, 85805, 143304], 'label': '77760.bo.1080.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '1080.bi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bi1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055230
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['270.v1', '360.v1', '360.bq1', '540.br1'], 'contains': ['2160.b1', '2160.j1', '2160.t1', '2160.z1', '2160.bh1', '2160.ch1', '2160.cp1', '3240.r1', '3240.bl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [442641104880, 442162067904, 85805, 80880, 143304], 'label': '77760.bo.1080.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '1080.bj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bj1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055458
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1296.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.e1', '648.i1'], 'contains': ['2592.b1', '2592.d1', '3888.c1', '6480.x1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [85805, 80787, 18764663042, 143304], 'label': '77760.bo.1296.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.e1', 'old_label': '1296.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.h1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 246055231
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.i1', '270.w1', '360.w1', '360.br1', '540.br1'], 'contains': ['2160.e1', '2160.k1', '2160.w1', '2160.bd1', '2160.bh1', '2160.cl1', '2160.cs1', '3240.s1', '3240.bm1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [113566924800, 88176252092, 143975, 40585, 143304], 'label': '77760.bo.1080.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '1080.bk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bk1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055232
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.x1', '360.x1', '360.bp1', '540.bt1'], 'contains': ['2160.p1', '2160.y1', '2160.bi1', '2160.bo1', '2160.bu1', '3240.q1', '3240.bn1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [518964004, 442641024000, 85805, 80787, 143304], 'label': '77760.bo.1080.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '1080.bl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055233
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.y1', '360.x1', '360.bq1', '540.bt1'], 'contains': ['2160.s1', '2160.bb1', '2160.bi1', '2160.bp1', '2160.bx1', '3240.r1', '3240.bn1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [442641024000, 442162022400, 85805, 80787, 143304], 'label': '77760.bo.1080.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.r1', 'old_label': '1080.bm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bm1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055234
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.j1', '270.z1', '360.y1', '360.br1', '540.bt1'], 'contains': ['2160.v1', '2160.bf1', '2160.bi1', '2160.bs1', '2160.by1', '3240.s1', '3240.bo1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [113566924800, 88176252092, 85805, 80787, 693], 'label': '77760.bo.1080.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '1080.bn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bn1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055235
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.z1', '360.ba1', '360.bb1', '360.bd1', '540.bz1', '540.bz2', '540.cm1'], 'contains': ['2160.bj1', '2160.bl1', '2160.bm1', '2160.cu1', '2160.dc1', '2160.ge1', '2160.gi1', '3240.t1', '3240.u1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [442641024148, 443120071554, 85805, 80880, 80787], 'label': '77760.bo.1080.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bj1', 'old_label': '1080.bo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bo1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055236
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.bo2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.bb2', '540.bz1', '540.bz2', '540.cm2'], 'contains': ['2160.bj1', '2160.bl1', '2160.bm1', '2160.cu2', '2160.dc2', '2160.ge2', '2160.gi2', '3240.t2', '3240.u2'], 'core': '4320.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [442641386755, 448908001949, 85805, 80880, 80787], 'label': '77760.bo.1080.bo2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.bo2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bo2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055237
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.bc1', '360.be1', '540.bx1', '540.by1', '540.bz2', '540.ca1', '540.cb1', '540.cc1', '540.cm1'], 'contains': ['2160.bj1', '2160.bk1', '2160.cx1', '2160.dj1', '2160.ec1', '3240.v1', '3240.w1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [183845, 87182277597, 143975, 375138172555, 80787], 'label': '77760.bo.1080.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '1080.bp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bp1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246055238
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.k1', '18.n1', '27.a1'], 'contains': ['108.n1', '108.r1', '324.g1', '540.cx1', '810.bu1'], 'core': '216.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [93924231093, 462320046985, 693], 'label': '77760.bo.54.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.g1', 'subgroup_fusion': None, 'weyl_group': '720.763'}
  • id: 246055239
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.bp2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.bc2', '540.bv1', '540.bw1', '540.bz1', '540.cc1', '540.cm2'], 'contains': ['2160.bj1', '2160.bk1', '2160.cx2', '2160.dj2', '2160.ec2', '3240.v2', '3240.w2'], 'core': '4320.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [442641024148, 448908001949, 85805, 80880, 80787], 'label': '77760.bo.1080.bp2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '1080.bp2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bp2', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055240
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.bf1', '360.bl1', '540.by1', '540.bz1', '540.cf1', '540.cg1', '540.ci1', '540.cj1', '540.cm1'], 'contains': ['2160.bk1', '2160.bl1', '2160.eb1', '2160.ed1', '2160.fq1', '3240.x1', '3240.y1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87181925066, 85805, 375138172555, 80880, 80787], 'label': '77760.bo.1080.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.bq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bq1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055241
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.bq2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.bf2', '540.bz2', '540.cd1', '540.ce1', '540.cj1', '540.cm2'], 'contains': ['2160.bk1', '2160.bl1', '2160.eb2', '2160.ed2', '2160.fq2', '3240.x2', '3240.y2'], 'core': '4320.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [442641386755, 85805, 80880, 80787, 448908283914], 'label': '77760.bo.1080.bq2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.bq2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bq2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055242
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.g1', '360.bg1', '540.bv1', '540.ca1', '540.cd1', '540.cf1', '540.cn1'], 'contains': ['2160.bk1', '2160.ej1', '2160.ep1', '3240.z1', '3240.bd1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [443120071204, 267845397242, 85805, 80880, 80787], 'label': '77760.bo.1080.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '1080.br1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.br1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246055243
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.o1', '360.bh1', '540.bv1', '540.cb1', '540.ce1', '540.cg1', '540.ch1', '540.cl1', '540.co1'], 'contains': ['2160.bk1', '2160.ek1', '2160.en1', '3240.ba1', '3240.be1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [88695170185, 482635561, 85805, 80880, 80787], 'label': '77760.bo.1080.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '1080.bs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bs1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246055244
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.p1', '360.bi1', '540.bw1', '540.by1', '540.cd1', '540.ck1', '540.co1'], 'contains': ['2160.bk1', '2160.el1', '2160.em1', '3240.bb1', '3240.bf1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [482635561, 85805, 80880, 80787, 88695348625], 'label': '77760.bo.1080.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.bt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bt1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055245
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.h1', '360.bj1', '540.bw1', '540.bx1', '540.ce1', '540.ci1', '540.cn1'], 'contains': ['2160.bk1', '2160.eo1', '2160.eq1', '3240.bc1', '3240.bg1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [443120071204, 267845679213, 85805, 80880, 80787], 'label': '77760.bo.1080.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.bu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bu1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055246
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.bk1', '540.bx1', '540.bz1', '540.bz2', '540.cf1', '540.ch1', '540.ck1', '540.cp1'], 'contains': ['2160.bk1', '2160.bm1', '2160.ef1', '2160.eh1', '2160.gl1', '3240.bh1', '3240.bi1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [442681124645, 355499159518, 183845, 143975, 80787], 'label': '77760.bo.1080.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.bv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bv1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055247
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.bm1', '360.bn1', '360.bo1', '540.ca1', '540.cc1', '540.ci1', '540.cj1', '540.ck1', '540.cl1', '540.cp1'], 'contains': ['2160.bk1', '2160.eg1', '2160.fb1', '3240.bj1', '3240.bk1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [183845, 274467962404, 143975, 268244605587, 80787], 'label': '77760.bo.1080.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '1080.bw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bw1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246055248
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gk1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.bp1', '360.bq1', '360.bs1', '540.cm1', '540.cm2'], 'contains': ['2160.o1', '2160.ba1', '2160.bj1', '2160.bl1', '2160.bn1', '2160.cb1', '2160.co1', '3240.bl1', '3240.bn1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [442641386187, 143975, 85805, 80787, 143304], 'label': '77760.bo.1080.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '1080.bx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bx1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055249
    {'ambient': '77760.bo', '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': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['20.a1', '30.e1'], 'contains': ['120.b1', '120.c1', '120.e1', '120.bk1', '120.bl1', '120.bv1', '120.by1', '180.a1', '180.g1', '540.o1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [143975, 80787, 174400208787, 93449036612, 180587232000, 83543730, 456053207518, 40349], 'label': '77760.bo.60.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '60.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.a1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246055250
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.i1', '360.br1', '360.bt1', '540.cm1', '540.cm2', '540.cn1', '540.co1', '540.cp1'], 'contains': ['2160.u1', '2160.be1', '2160.bk1', '2160.bm1', '2160.bn1', '2160.cj1', '2160.cr1', '3240.bm1', '3240.bo1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [274467962404, 143975, 85805, 80787, 143304], 'label': '77760.bo.1080.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.by1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.by1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055251
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.bl1', '360.bu1', '360.bz1', '540.bt1'], 'contains': ['2160.bo1', '2160.bx1', '2160.by1', '2160.cy1', '2160.gd1', '3240.bp1', '3240.bq1', '3240.br1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [224184, 368871153961, 174436559403, 80787, 375138086400], 'label': '77760.bo.1080.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '1080.bz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bz1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055252
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['270.bm1', '360.bu1', '360.ca1', '540.bt1'], 'contains': ['2160.bp1', '2160.bu1', '2160.by1', '2160.dm1', '2160.fr1', '3240.bp1', '3240.bt1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [375138091561, 224184, 368871148800, 174436559403, 80787], 'label': '77760.bo.1080.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '1080.ca1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ca1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055253
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.bu1', '360.cb1'], 'contains': ['2160.bq1', '2160.bv1', '2160.bz1', '2160.do1', '2160.fv1', '3240.br1', '3240.bt1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [456053069398, 93448938387, 598, 174400128000, 180587272349], 'label': '77760.bo.1080.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.cb1', 'old_label': '1080.cb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.cb1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055254
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.bu1', '360.cc1', '540.j1'], 'contains': ['2160.br1', '2160.bw1', '2160.ca1', '2160.dq1', '2160.fx1', '3240.bq1', '3240.bt1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [456053069398, 598, 174400128000, 180587272349, 93448857600], 'label': '77760.bo.1080.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.j1', 'old_label': '1080.cc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.cc1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055255
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.l1', '270.bn1', '360.bv1', '360.cd1', '360.ce1', '540.bt1'], 'contains': ['2160.bo1', '2160.bp1', '2160.bs1', '2160.de1', '2160.dr1', '2160.dx1', '2160.ey1', '3240.bs1', '3240.bu1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [518964004, 442641024000, 998000787, 80787, 143304], 'label': '77760.bo.1080.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '1080.cd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.cd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055256
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.bv1', '360.cf1', '360.cg1', '540.j1', '540.cs1', '540.ct1'], 'contains': ['2160.br1', '2160.bt1', '2160.dw1', '2160.ea1', '2160.fl1', '3240.bu1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [83462998, 598, 174400128000, 180587232000, 93448857600], 'label': '77760.bo.1080.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '1080.ce1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ce1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246055257
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.m1', '270.bo1', '360.bw1', '360.ch1', '540.bt1'], 'contains': ['2160.bs1', '2160.bu1', '2160.bx1', '2160.ew1', '2160.gj1', '3240.bv1', '3240.cb1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [375138091561, 224184, 368871153961, 174436559403, 80787], 'label': '77760.bo.1080.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '1080.cf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.cf1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055258
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.j1', '360.ci1', '360.cj1', '540.bu1', '540.cq1', '540.cr1', '540.cu1', '540.cv1', '540.cw1', '540.cy1'], 'contains': ['2160.fd1', '3240.cc1', '3240.cd1', '3240.ce1', '4320.i1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [274467962404, 194518195200, 268244605587, 80787, 143304], 'label': '77760.bo.1080.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '1080.cg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.cg1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246055259
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.bw1', '360.ck1', '540.j1', '540.cs1', '540.cx1'], 'contains': ['2160.bt1', '2160.bw1', '2160.fk1', '2160.gc1', '3240.cb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [456053154955, 174400128000, 180587232000, 93448857600, 693], 'label': '77760.bo.1080.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.e1', 'old_label': '1080.ch1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ch1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246055260
    {'ambient': '77760.bo', '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': '25920.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.b1', '20.b1', '30.e1'], 'contains': ['120.b1', '120.d1', '120.bj1', '120.bn1', '120.bw1', '180.b1', '180.h1', '540.r1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [143975, 80787, 174400208787, 93449036612, 180587232000, 456053207518, 83606375, 40349], 'label': '77760.bo.60.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '60.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.b1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 246055261
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.n1', '360.bx1', '360.cl1', '360.cn1', '540.k1', '540.ct1', '540.cx1'], 'contains': ['2160.bt1', '2160.fm1', '2160.fn1', '9720.q1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [280259481600, 88695272904, 482773704, 193999420104, 143304], 'label': '77760.bo.1080.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '1080.ci1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ci1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246055262
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.by1', '360.cm1', '540.k1', '540.cs1'], 'contains': ['2160.bt1', '2160.fo1', '9720.r1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [280259481600, 482854584, 224184, 193999500984, 88695348625], 'label': '77760.bo.1080.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.e1', 'old_label': '1080.cj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.cj1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246055263
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.bz1', '360.ca1', '360.co1', '540.cm1', '540.cz1', '540.cz2'], 'contains': ['2160.cb1', '2160.co1', '2160.cr1', '2160.cu1', '2160.cx1', '2160.fq1', '2160.ge1', '3240.bp1', '3240.cf1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [442641386187, 143975, 443120245054, 80787, 143304], 'label': '77760.bo.1080.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bj1', 'old_label': '1080.ck1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ck1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055264
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ck2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.co2', '540.cm2', '540.cz1', '540.cz2'], 'contains': ['2160.cb1', '2160.co1', '2160.cr1', '2160.cu2', '2160.cx2', '2160.fq2', '2160.ge2', '3240.bp2', '3240.cf2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [448908278999, 224184, 442641300629, 143975, 80787], 'label': '77760.bo.1080.ck2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.ck2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ck2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055265
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['270.bt1', '360.bz1', '360.cc1', '540.br1'], 'contains': ['2160.cd1', '2160.cp1', '2160.cs1', '2160.cv1', '2160.da1', '2160.ft1', '2160.gf1', '3240.bq1', '3240.cf1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [368871287518, 224184, 224515, 174436640184, 375138310915], 'label': '77760.bo.1080.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '1080.cl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.cl1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055266
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['270.bu1', '360.bz1', '360.cb1'], 'contains': ['2160.ce1', '2160.cq1', '2160.ct1', '2160.cw1', '2160.db1', '2160.fu1', '2160.gg1', '3240.br1', '3240.cf1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [224184, 998139594, 224515, 519235320, 442641305788], 'label': '77760.bo.1080.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.cm1', 'old_label': '1080.cm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.cm1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055285
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.bb1', '360.ct1', '540.de1', '540.di1', '540.ef1'], 'contains': ['2160.ck1', '2160.es1', '2160.et1', '3240.by1', '3240.cp1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [482854444, 88695353644, 80787, 143304, 179159], 'label': '77760.bo.1080.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '1080.cz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.cz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055267
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.cd1', '360.cp1', '540.cm1', '540.cz2', '540.da1', '540.db1', '540.df1', '540.dh1', '540.dj1'], 'contains': ['2160.cb1', '2160.cj1', '2160.dc1', '2160.dj1', '2160.ed1', '3240.bs1', '3240.cg1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [443120071204, 442641024148, 80880, 80787, 143304], 'label': '77760.bo.1080.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.cn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.cn1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055268
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.cn2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.cp2', '540.cm2', '540.cz1', '540.dc1', '540.dd1', '540.dj1'], 'contains': ['2160.cb1', '2160.cj1', '2160.dc2', '2160.dj2', '2160.ed2', '3240.bs2', '3240.cg2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [448908278999, 362615, 442641024148, 80880, 80787], 'label': '77760.bo.1080.cn2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.cn2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.cn2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055269
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.ce1', '360.cp1', '540.dg1', '540.di1', '540.dk1'], 'contains': ['2160.cc1', '2160.ck1', '2160.dd1', '2160.dk1', '2160.ee1', '3240.bs1', '3240.ch1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [443120204759, 442641386284, 80787, 143304, 179159], 'label': '77760.bo.1080.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '1080.co1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.co1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055270
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.co2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.cp2', '540.de1', '540.dk1'], 'contains': ['2160.cc1', '2160.ck1', '2160.dd2', '2160.dk2', '2160.ee2', '3240.bs2', '3240.ch2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [448908278999, 442641386284, 80787, 143304, 179159], 'label': '77760.bo.1080.co2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '1080.co2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.co2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246055271
    {'ambient': '77760.bo', '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': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.c1', '20.c1', '30.e1'], 'contains': ['120.c1', '120.d1', '120.bx1', '120.bz1', '120.ca1', '180.c1', '180.n1', '540.bb1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [143975, 80787, 174400208787, 93449036612, 180587232000, 456053154955, 83543730, 40349], 'label': '77760.bo.60.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '60.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.c1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246055272
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['270.bv1', '360.ca1', '360.cb1', '360.cc1', '540.br1'], 'contains': ['2160.ch1', '2160.cn1', '2160.cs1', '2160.dl1', '2160.dn1', '2160.fp1', '2160.fz1', '3240.bt1', '3240.cf1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [224184, 375138225118, 224515, 368871373315, 174436640184], 'label': '77760.bo.1080.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '1080.cp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.cp1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055273
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.o1', '270.by1', '360.cd1', '360.cf1', '540.br1'], 'contains': ['2160.cd1', '2160.ch1', '2160.cl1', '2160.dh1', '2160.ds1', '2160.dy1', '2160.ez1', '3240.bu1', '3240.cg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [174436640184, 368871194304, 80880, 375138086400, 143304], 'label': '77760.bo.1080.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '1080.cq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.cq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055274
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.p1', '270.bz1', '360.ce1', '360.cg1'], 'contains': ['2160.cf1', '2160.ci1', '2160.cm1', '2160.di1', '2160.dt1', '2160.dz1', '2160.fa1', '3240.bu1', '3240.ch1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [224184, 375138311012, 368871373412, 174436640184, 224612], 'label': '77760.bo.1080.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ce1', 'old_label': '1080.cr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.cr1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055275
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ch1', '360.cq1', '540.cm1', '540.cz1', '540.da1', '540.dr1', '540.du1', '540.dx1', '540.ea1'], 'contains': ['2160.cj1', '2160.co1', '2160.eb1', '2160.ec1', '2160.gi1', '3240.bv1', '3240.ci1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87182202116, 143975, 375138270474, 80787, 143304], 'label': '77760.bo.1080.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.cs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.cs1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055276
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.cs2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.cq2', '540.cm2', '540.cz2', '540.ds1', '540.dt1', '540.ea1'], 'contains': ['2160.cj1', '2160.co1', '2160.eb2', '2160.ec2', '2160.gi2', '3240.bv2', '3240.ci2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [178680, 442641300482, 143975, 448908284158, 80787], 'label': '77760.bo.1080.cs2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.cs2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.cs2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055277
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.cr1', '540.cp1', '540.cz1', '540.cz2', '540.db1', '540.dr1', '540.dv1', '540.eb1'], 'contains': ['2160.cj1', '2160.cr1', '2160.ef1', '2160.eg1', '2160.gl1', '3240.bw1', '3240.cj1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [178680, 143975, 268244605587, 274468002505, 80787], 'label': '77760.bo.1080.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.ct1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ct1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055278
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.k1', '360.cs1', '540.cn1', '540.dc1', '540.df1', '540.dr1', '540.ds1'], 'contains': ['2160.cj1', '2160.ej1', '2160.eq1', '3240.bx1', '3240.ck1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [443120071204, 362615, 80880, 80787, 267845674052], 'label': '77760.bo.1080.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.cu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.cu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055279
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.z1', '360.ct1', '540.co1', '540.dc1', '540.dh1', '540.dt1', '540.du1', '540.dv1', '540.ee1'], 'contains': ['2160.cj1', '2160.ek1', '2160.el1', '3240.by1', '3240.cl1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [482854444, 143975, 88695353644, 80787, 143304], 'label': '77760.bo.1080.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.cv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.cv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055280
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.ba1', '360.cu1', '540.co1', '540.da1', '540.dd1', '540.ds1', '540.eb1'], 'contains': ['2160.cj1', '2160.em1', '2160.en1', '3240.bz1', '3240.cm1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [482808988, 224184, 143975, 80787, 88695348625], 'label': '77760.bo.1080.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.cw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.cw1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055281
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.l1', '360.cv1', '540.cn1', '540.db1', '540.dd1', '540.dt1', '540.dx1'], 'contains': ['2160.cj1', '2160.eo1', '2160.ep1', '3240.ca1', '3240.cn1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [267845679358, 443120250115, 143975, 80787, 143304], 'label': '77760.bo.1080.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.cx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.cx1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055282
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.b1', '12.d1', '12.m1', '18.a1', '18.c1', '36.c1', '60.b1', '90.c1'], 'core': '12.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [93924369357, 143975, 85805, 80787, 462320328386], 'label': '77760.bo.6.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1', 'subgroup_fusion': None, 'weyl_group': '8640.t'}
  • id: 246055283
    {'ambient': '77760.bo', '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': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['30.a1', '30.c1', '30.f1'], 'contains': ['120.m1', '120.bh1', '120.bp1', '180.d1', '180.ba1', '180.bb1', '180.bc1', '240.e1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [355462738109, 87660962042, 143975, 375138270474, 85805, 80880, 80787, 462320328386], 'label': '77760.bo.60.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '60.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.d1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246055284
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.m1', '360.cs1', '540.de1', '540.dg1'], 'contains': ['2160.ck1', '2160.er1', '2160.eu1', '3240.bx1', '3240.co1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [443120204759, 224184, 80787, 267845674052, 179159], 'label': '77760.bo.1080.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '1080.cy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.cy1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055457
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1296.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.e1', '648.h1'], 'contains': ['2592.a1', '2592.c1', '2592.e1', '3888.c1', '6480.w1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [143975, 5066, 18764663042, 143304], 'label': '77760.bo.1296.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d1', 'old_label': '1296.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.g1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 246055286
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.q1', '270.cb1', '360.ch1', '360.ck1', '540.br1'], 'contains': ['2160.cl1', '2160.cn1', '2160.cp1', '2160.ev1', '2160.ex1', '2160.ga1', '2160.gh1', '3240.cb1', '3240.ci1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [368871287518, 224184, 375138225118, 224515, 174436640184], 'label': '77760.bo.1080.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '1080.da1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.da1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055287
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ci1', '360.cw1', '540.cp1', '540.df1', '540.dj1', '540.dx1', '540.ea1', '540.eb1', '540.ee1'], 'contains': ['2160.cj1', '2160.eh1', '2160.fb1', '3240.cc1', '3240.cq1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [268244570163, 80880, 80787, 274467916948, 143304], 'label': '77760.bo.1080.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '1080.db1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.db1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055288
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.cj1', '360.cw1', '540.dg1', '540.dk1', '540.ef1'], 'contains': ['2160.ck1', '2160.ei1', '2160.fc1', '3240.cc1', '3240.cr1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [274467962404, 268244605587, 80787, 143304, 179159], 'label': '77760.bo.1080.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '1080.dc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.dc1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055289
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.n1', '360.ci1', '540.bs1', '540.dl1', '540.dp1', '540.dw1', '540.dy1', '540.ec1', '540.eg1'], 'contains': ['2160.fg1', '3240.cd1', '3240.cq1', '4320.n1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [442681258052, 362615, 355419504452, 355499101444, 45363], 'label': '77760.bo.1080.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '1080.dd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.dd1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246055290
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ci1', '540.dm1', '540.dz1', '540.ed1'], 'contains': ['2160.fh1', '3240.ce1', '3240.cq1', '4320.o1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [442681258052, 362615, 355419549955, 355499101444, 45363], 'label': '77760.bo.1080.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.z1', 'old_label': '1080.de1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.de1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246055291
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.o1', '360.cj1', '540.dn1', '540.dq1', '540.eh1'], 'contains': ['2160.fi1', '3240.cd1', '3240.cr1', '4320.p1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [355419504452, 224184, 355499245412, 442681164984, 224612], 'label': '77760.bo.1080.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '1080.df1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.df1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246055292
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.cj1', '540.do1'], 'contains': ['2160.fj1', '3240.ce1', '3240.cr1', '4320.q1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [355419549955, 224184, 355499245412, 442681164984, 224612], 'label': '77760.bo.1080.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.cd1', 'old_label': '1080.dg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.dg1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 246055293
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.cx1', '540.p1', '540.bz2', '540.cz2'], 'contains': ['2160.cu2', '2160.cx1', '2160.dc1', '2160.fq2', '2160.ge1', '2160.gi2', '2160.gl1', '3240.cs1', '3240.ct1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [461841090505, 462320225425, 19679125948, 80880, 80787], 'label': '77760.bo.1080.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bj1', 'old_label': '1080.dh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.dh1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055294
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.e1', '30.b1', '30.c1', '30.g1'], 'contains': ['120.m1', '120.bi1', '120.bq1', '180.e1', '180.y1', '180.bd1', '240.h1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [143975, 80787, 87182277125, 375138270474, 85805, 482635561, 188331136563, 80880], 'label': '77760.bo.60.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '60.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.e1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246055295
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.dh2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.cx1', '540.p2', '540.bz1', '540.cz2'], 'contains': ['2160.cu1', '2160.cx2', '2160.dc1', '2160.fq1', '2160.ge2', '2160.gi2', '2160.gl1', '3240.cs2', '3240.ct1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [461841090505, 143975, 462320328958, 19679125948, 80787], 'label': '77760.bo.1080.dh2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bj1', 'old_label': '1080.dh2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.dh2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055296
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.dh3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.cx2', '540.p1', '540.bz1', '540.cz1'], 'contains': ['2160.cu2', '2160.cx2', '2160.dc2', '2160.fq1', '2160.ge1', '2160.gi1', '2160.gl1', '3240.cs3', '3240.ct2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [19679068105, 143975, 448908284158, 462320328485, 80787], 'label': '77760.bo.1080.dh3', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bj1', 'old_label': '1080.dh3', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.dh3', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055297
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.dh4', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.cx3', '540.p2', '540.bz2', '540.cz1'], 'contains': ['2160.cu1', '2160.cx1', '2160.dc2', '2160.fq2', '2160.ge2', '2160.gi1', '2160.gl1', '3240.cs4', '3240.ct3'], 'core': '8640.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [461841090505, 462320323652, 143975, 19679125948, 80787], 'label': '77760.bo.1080.dh4', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bj1', 'old_label': '1080.dh4', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.dh4', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055298
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.ec1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.cy1', '540.s1', '540.bz1', '540.cz1', '540.ei1', '540.el1', '540.er1', '540.fd1'], 'contains': ['2160.cu1', '2160.cu2', '2160.dj2', '2160.eb1', '2160.ef1', '3240.cu1', '3240.cw1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841090505, 462320323320, 19679028004, 143975, 80787], 'label': '77760.bo.1080.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.di1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.di1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055299
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.di2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.ec1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.cy2', '540.s1', '540.bz2', '540.cz2', '540.ek1', '540.ep1', '540.ev1', '540.ez1'], 'contains': ['2160.cu1', '2160.cu2', '2160.dj1', '2160.eb2', '2160.ef1', '3240.cu2', '3240.cw2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [462320225425, 19678982548, 461841188401, 80880, 80787], 'label': '77760.bo.1080.di2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.di2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.di2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055300
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.ce2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bj1', '360.cz1', '540.r1', '540.by1', '540.da1', '540.ej1', '540.eq1', '540.ev1', '540.fd1'], 'contains': ['2160.dj1', '2160.eb1', '2160.em1', '3240.cv1', '3240.cy1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [83601118, 87262035388, 143975, 456053212775, 80787], 'label': '77760.bo.1080.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.dj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.dj1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246055301
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.cy1', '540.p1', '540.cc1', '540.cz1', '540.en1', '540.er1', '540.es1', '540.fg1'], 'contains': ['2160.cx1', '2160.cx2', '2160.dj2', '2160.ec1', '2160.eg1', '3240.cw1', '3240.cx1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [19679201425, 143975, 448908284158, 462320328958, 80787], 'label': '77760.bo.1080.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '1080.dk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.dk1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246055302
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.dk2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.cy2', '540.p2', '540.cc1', '540.cz2', '540.eo1', '540.eq1', '540.ew1', '540.fa1'], 'contains': ['2160.cx1', '2160.cx2', '2160.dj1', '2160.ec2', '2160.eg1', '3240.cw2', '3240.cx2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841223825, 19679028004, 143975, 462320328958, 80787], 'label': '77760.bo.1080.dk2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '1080.dk2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.dk2', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246055303
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bk1', '360.cz1', '540.o1', '540.cb1', '540.da1', '540.em1', '540.ep1', '540.ew1', '540.fg1'], 'contains': ['2160.dj1', '2160.ec1', '2160.en1', '3240.cy1', '3240.cz1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [87262035388, 456053154955, 83606375, 143975, 80787], 'label': '77760.bo.1080.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '1080.dl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.dl1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246055304
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.da1', '540.p1', '540.bz1', '540.dj1', '540.ei1', '540.en1', '540.et1', '540.fl1'], 'contains': ['2160.dc1', '2160.dc2', '2160.dj2', '2160.ed1', '2160.eh1', '3240.da1', '3240.dc1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [448908278999, 462320323320, 19679028004, 143975, 80787], 'label': '77760.bo.1080.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.dm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.dm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055305
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['20.a1', '30.e1'], 'contains': ['120.k1', '120.n1', '120.p1', '120.bj1', '120.bl1', '120.bx1', '120.by1', '180.f1', '180.g1', '540.by1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [180587277504, 456053074316, 93448857748, 83543044, 174400173363, 85805, 80880, 80787], 'label': '77760.bo.60.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '60.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.f1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246055306
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.dm2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.da2', '540.p2', '540.bz2', '540.dj1', '540.ej1', '540.em1', '540.ex1', '540.fb1'], 'contains': ['2160.dc1', '2160.dc2', '2160.dj1', '2160.ed2', '2160.eh1', '3240.da2', '3240.dc2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [448908278999, 462320052004, 19679345155, 80880, 80787], 'label': '77760.bo.1080.dm2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.dm2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.dm2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055307
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.da1', '540.dk1', '540.eu1', '540.fm1'], 'contains': ['2160.dd1', '2160.dd2', '2160.dk2', '2160.ee1', '2160.ei1', '3240.da1', '3240.dd1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [462320323467, 19679028004, 461841148348, 80787, 179159], 'label': '77760.bo.1080.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '1080.dn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.dn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055308
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.dn2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.da2', '540.dk1', '540.ey1', '540.fc1'], 'contains': ['2160.dd1', '2160.dd2', '2160.dk1', '2160.ee2', '2160.ei1', '3240.da2', '3240.dd2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [448908278999, 19679206444, 462320323467, 80787, 179159], 'label': '77760.bo.1080.dn2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '1080.dn2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.dn2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055309
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bl1', '360.db1', '540.o1', '540.by1', '540.dh1', '540.ek1', '540.eo1', '540.ex1', '540.fl1'], 'contains': ['2160.dj1', '2160.ed1', '2160.el1', '3240.db1', '3240.de1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [83543730, 87262035388, 143975, 456053212775, 80787], 'label': '77760.bo.1080.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.do1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.do1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246055310
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.bm1', '360.db1', '540.di1', '540.ey1', '540.fm1'], 'contains': ['2160.dk1', '2160.ee1', '2160.et1', '3240.db1', '3240.df1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87262035144, 456053150130, 83687012, 80787, 179159], 'label': '77760.bo.1080.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '1080.dp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.dp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055311
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.ce2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.dc1', '540.q1', '540.bx1', '540.db1', '540.em1', '540.eo1', '540.ez1', '540.fd1'], 'contains': ['2160.dj1', '2160.ef1', '2160.eo1', '3240.dg1', '3240.dh1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [482768881, 80880, 80787, 375138086400, 87182000787], 'label': '77760.bo.1080.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.dq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.dq1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246055312
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.dc1', '540.n1', '540.ca1', '540.db1', '540.ej1', '540.ek1', '540.fa1', '540.fg1'], 'contains': ['2160.dj1', '2160.eg1', '2160.ep1', '3240.dh1', '3240.di1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [443120071204, 442641024148, 180667151546, 80880, 80787], 'label': '77760.bo.1080.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '1080.dr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.dr1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246055313
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.dd1', '540.n1', '540.bx1', '540.df1', '540.ep1', '540.eq1', '540.fb1', '540.fl1'], 'contains': ['2160.dj1', '2160.eh1', '2160.eq1', '3240.dj1', '3240.dk1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [482808988, 143975, 87182201788, 80787, 375138230375], 'label': '77760.bo.1080.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.ds1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ds1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246055314
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.dd1', '540.dg1', '540.fc1', '540.fm1'], 'contains': ['2160.dk1', '2160.ei1', '2160.eu1', '3240.dj1', '3240.dl1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [482808988, 87182201544, 375138311012, 80787, 179159], 'label': '77760.bo.1080.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '1080.dt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.dt1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055315
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.du1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.de1', '540.l1', '540.bv1', '540.dc1', '540.el1', '540.es1', '540.et1', '540.fy1'], 'contains': ['2160.dj2', '2160.ej1', '2160.ek1', '3240.dm1', '3240.dp1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [7185104880, 462320052004, 19678982548, 80880, 80787], 'label': '77760.bo.1080.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '1080.du1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.du1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055316
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '20.b1', '30.e1'], 'contains': ['120.k1', '120.o1', '120.bk1', '120.bn1', '120.bz1', '180.h1', '180.i1', '540.cb1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [143975, 80787, 174400208787, 93449036612, 180587232000, 456053154955, 183845, 83606375], 'label': '77760.bo.60.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '60.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.g1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246055317
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.df1', '540.m1', '540.bw1', '540.dc1', '540.er1', '540.fl1'], 'contains': ['2160.dj2', '2160.el1', '2160.eq1', '3240.dn1', '3240.dq1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [462320052004, 19678982548, 80880, 80787, 7185202680], 'label': '77760.bo.1080.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.dv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.dv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055318
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dp1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.dg1', '540.l1', '540.bw1', '540.dd1', '540.en1', '540.fd1'], 'contains': ['2160.dj2', '2160.em1', '2160.eo1', '3240.do1', '3240.dr1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [7185029309, 462320323320, 19679028004, 143975, 80787], 'label': '77760.bo.1080.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.dw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.dw1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055319
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.dg1', '540.m1', '540.bv1', '540.dd1', '540.ei1', '540.fg1'], 'contains': ['2160.dj2', '2160.en1', '2160.ep1', '3240.do1', '3240.ds1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [7185029309, 462320052004, 19678982548, 80880, 80787], 'label': '77760.bo.1080.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '1080.dx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.dx1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246055320
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.dy1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.de1', '540.de1', '540.eu1', '540.fz1'], 'contains': ['2160.dk2', '2160.er1', '2160.es1', '3240.dm1', '3240.dt1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [462320323467, 7185024000, 19679028004, 80787, 179159], 'label': '77760.bo.1080.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bi1', 'old_label': '1080.dy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.dy1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055321
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.df1', '540.de1', '540.fm1'], 'contains': ['2160.dk2', '2160.et1', '2160.eu1', '3240.dn1', '3240.du1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [462320323467, 19679028004, 80787, 7185202680, 179159], 'label': '77760.bo.1080.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '1080.dz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.dz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055322
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.dj2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.dh1', '360.do1', '540.q1', '540.ca1', '540.df1', '540.ev1', '540.ew1', '540.ex1', '540.fy1'], 'contains': ['2160.dj1', '2160.ej1', '2160.fb1', '3240.dv1', '3240.dw1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [442641386187, 180667146387, 443120250115, 143975, 80787], 'label': '77760.bo.1080.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '1080.ea1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ea1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246055323
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.dk2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.dh1', '360.dp1', '540.dg1', '540.ey1', '540.fz1'], 'contains': ['2160.dk1', '2160.er1', '2160.fc1', '3240.dv1', '3240.dx1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [87182201544, 482676004, 375138311012, 80787, 179159], 'label': '77760.bo.1080.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bi1', 'old_label': '1080.eb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.eb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055324
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.dj2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.bn1', '360.di1', '540.r1', '540.cb1', '540.dh1', '540.ez1', '540.fa1', '540.fb1', '540.fy1'], 'contains': ['2160.dj1', '2160.ek1', '3240.dy1', '3240.dz1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [87262035388, 83606375, 143975, 456053212775, 80787], 'label': '77760.bo.1080.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '1080.ec1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ec1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246055325
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.dk2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.bo1', '360.di1', '540.di1', '540.fc1', '540.fz1'], 'contains': ['2160.dk1', '2160.es1', '3240.dy1', '3240.ea1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [87262035144, 83687012, 456053293412, 80787, 179159], 'label': '77760.bo.1080.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bi1', 'old_label': '1080.ed1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ed1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055326
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.ee1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.dj1', '360.dk1', '360.dl1', '540.s1', '540.cc1', '540.dj1', '540.fd1', '540.fg1', '540.fl1', '540.fy1'], 'contains': ['2160.dj1', '2160.dj2', '2160.fb1', '3240.eb1', '3240.ec1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [462320323320, 19679028004, 143975, 461841050404, 80787], 'label': '77760.bo.1080.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '1080.ee1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ee1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055327
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['30.b1', '30.d1', '30.f1'], 'contains': ['120.m1', '120.bp1', '120.br1', '180.j1', '180.bj1', '180.bn1', '240.m1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [183845, 355462871189, 87660962042, 143975, 375138270474, 80880, 80787, 462320328386], 'label': '77760.bo.60.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '60.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.h1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246055328
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.ef1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.dl1', '360.dm1', '360.dn1', '540.dk1', '540.fm1', '540.fz1'], 'contains': ['2160.dk1', '2160.dk2', '2160.fc1', '3240.eb1', '3240.ed1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [462320323467, 19679028004, 448908278667, 80787, 179159], 'label': '77760.bo.1080.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.k1', 'old_label': '1080.ef1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ef1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055329
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.cj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.dj1', '360.dm1', '540.t1', '540.cq1', '540.fh1', '540.fn1', '540.ga1'], 'contains': ['2160.fd1', '3240.eb1', '3240.ee1', '3240.ef1', '4320.t1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [355462732800, 462320052004, 87661002387, 80787, 375138086400], 'label': '77760.bo.1080.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '1080.eg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.eg1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246055330
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.dj1', '360.dk1', '360.dn1', '540.u1', '540.fi1', '540.fo1'], 'contains': ['2160.fe1', '3240.eb1', '3240.eg1', '4320.u1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [19679028004, 462320052004, 461841050404, 262496505748, 80787], 'label': '77760.bo.1080.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1', 'old_label': '1080.eh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.eh1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246055331
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.dk1', '360.dm1', '360.dn1', '540.fp1'], 'contains': ['2160.ff1', '3240.eb1', '3240.eh1', '4320.v1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [262496649331, 19679028004, 462320052004, 461841050404, 80787], 'label': '77760.bo.1080.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.bb1', 'old_label': '1080.ei1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ei1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 246055332
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.dj1', '540.a1', '540.v1', '540.dl1', '540.fe1', '540.fj1', '540.fq1', '540.gb1'], 'contains': ['2160.fg1', '3240.ec1', '3240.ee1', '3240.eg1', '4320.w1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841004800, 179012, 19678982400, 462320323320, 262496684612], 'label': '77760.bo.1080.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '1080.ej1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ej1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246055333
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.dj1', '540.dm1', '540.ff1', '540.fk1'], 'contains': ['2160.fh1', '3240.ec1', '3240.ef1', '3240.eg1', '4320.x1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [461841004800, 179012, 262496730115, 19678982400, 462320323320], 'label': '77760.bo.1080.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.z1', 'old_label': '1080.ek1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ek1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246055334
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.dm1', '540.dn1', '540.fr1', '540.gc1'], 'contains': ['2160.fi1', '3240.ed1', '3240.ee1', '3240.eh1', '4320.y1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841004800, 262496730212, 19678982400, 462320323467, 224612], 'label': '77760.bo.1080.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '1080.el1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.el1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246055335
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.dm1', '540.do1'], 'contains': ['2160.fj1', '3240.ed1', '3240.ef1', '3240.eh1', '4320.z1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [462320368684, 375138265559, 355462813587, 87660921600, 179159], 'label': '77760.bo.1080.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.cd1', 'old_label': '1080.em1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.em1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 246055336
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.cj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.p1', '360.do1', '360.dp1', '540.w1', '540.cr1', '540.ft1', '540.fv1', '540.ga1'], 'contains': ['2160.fd1', '3240.dv1', '3240.ei1', '4320.ba1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [443120071204, 180667146387, 442641024000, 442162022400, 80787], 'label': '77760.bo.1080.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '1080.en1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.en1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246055337
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.q1', '360.do1', '540.b1', '540.x1', '540.dp1', '540.fs1', '540.fu1', '540.fw1', '540.gb1'], 'contains': ['2160.fg1', '3240.dw1', '3240.ei1', '4320.bb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [442641386187, 443120169575, 143975, 442162022400, 180667065600], 'label': '77760.bo.1080.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '1080.eo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.eo1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246055338
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.f1', '30.a1', '30.d1', '30.g1'], 'contains': ['120.m1', '120.bq1', '120.bs1', '180.k1', '180.bk1', '180.bl1', '180.bm1', '240.n1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [143975, 80787, 87182277125, 375138172555, 85805, 482635561, 188331136563, 80880], 'label': '77760.bo.60.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '60.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.i1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246055339
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.r1', '360.dp1', '540.dq1', '540.fx1', '540.gc1'], 'contains': ['2160.fi1', '3240.dx1', '3240.ei1', '4320.bc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [443120204759, 442641386284, 442162022400, 180667065600, 179159], 'label': '77760.bo.1080.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '1080.ep1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ep1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246055340
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.w1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.dq1', '360.dr1', '360.ds1', '540.c1', '540.d1', '540.cs1'], 'contains': ['2160.ea1', '2160.fk1', '2160.fo1', '9720.w1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [456053068800, 83548555, 174400128000, 180587232000, 93448857600], 'label': '77760.bo.1080.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '1080.eq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.eq1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246055341
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.dt1', '360.du1', '360.dv1', '540.c1', '540.ct1'], 'contains': ['2160.ea1', '2160.fl1', '2160.fn1', '9720.y1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [456053069398, 174400128000, 83462400, 180587232000, 93448857600], 'label': '77760.bo.1080.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '1080.er1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.er1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246055342
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1', '360.dw1', '360.dx1', '360.dy1', '540.d1', '540.ct1'], 'contains': ['2160.ea1', '2160.fm1', '9720.bf1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 10, 'diagramx': None, 'generators': [456053068800, 174400128000, 83462400, 180587232000, 93448857600], 'label': '77760.bo.1080.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '1080.es1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.es1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246055343
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.dz1', '540.p1', '540.cj1', '540.cz2', '540.ek1', '540.gd1', '540.gh1', '540.gq1'], 'contains': ['2160.eb2', '2160.ed1', '2160.eg1', '2160.fq1', '2160.fq2', '3240.ej1', '3240.et1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841090505, 19678982548, 462320328958, 80880, 80787], 'label': '77760.bo.1080.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.et1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.et1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055344
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.et2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.dz2', '540.p2', '540.cj1', '540.cz1', '540.ej1', '540.ge1', '540.gi1', '540.gn1'], 'contains': ['2160.eb1', '2160.ed2', '2160.eg1', '2160.fq1', '2160.fq2', '3240.ej2', '3240.et2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841223825, 462320323891, 19679028004, 143975, 80787], 'label': '77760.bo.1080.et2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.et2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.et2', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055345
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bv1', '360.ea1', '540.o1', '540.cg1', '540.da1', '540.ei1', '540.gg1', '540.gn1', '540.gq1'], 'contains': ['2160.eb1', '2160.ed1', '2160.en1', '3240.ek1', '3240.eu1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87261834480, 83467916, 456053150130, 80880, 80787], 'label': '77760.bo.1080.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.eu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.eu1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246055346
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.ce2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.eb1', '540.q1', '540.cf1', '540.dr1', '540.el1', '540.ev1', '540.gg1', '540.gi1'], 'contains': ['2160.eb1', '2160.ef1', '2160.ej1', '3240.el1', '3240.ey1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [482635916, 375138172555, 80880, 80787, 87182000787], 'label': '77760.bo.1080.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.ev1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ev1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246055347
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ec1', '540.n1', '540.ci1', '540.dr1', '540.eq1', '540.er1', '540.ge1', '540.gq1'], 'contains': ['2160.eb1', '2160.eg1', '2160.eq1', '3240.em1', '3240.ez1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [482849425, 143975, 375138270474, 87182201788, 80787], 'label': '77760.bo.1080.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.ew1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ew1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246055348
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ed1', '540.n1', '540.cf1', '540.dx1', '540.ei1', '540.ej1', '540.gj1', '540.ha1'], 'contains': ['2160.eb1', '2160.eh1', '2160.ep1', '3240.en1', '3240.fb1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [482711730, 375138172555, 80880, 80787, 87182000787], 'label': '77760.bo.1080.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.ex1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ex1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246055349
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['30.a1', '30.b1', '30.h1'], 'contains': ['120.m1', '120.bt1', '120.bu1', '180.l1', '180.bo1', '180.bp1', '180.bq1', '240.q1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [374659361758, 183845, 87182277597, 143975, 19203926428, 87657516984, 80880, 80787], 'label': '77760.bo.60.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '60.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.j1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246055350
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dp1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.ee1', '540.l1', '540.cd1', '540.ds1', '540.ev1', '540.gh1'], 'contains': ['2160.eb2', '2160.ej1', '2160.em1', '3240.eo1', '3240.fd1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [7185104880, 19678982548, 462320328958, 80880, 80787], 'label': '77760.bo.1080.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.ey1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ey1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055351
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dp1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.ef1', '540.l1', '540.ce1', '540.dt1', '540.ez1', '540.gd1', '540.gl1', '540.hf1'], 'contains': ['2160.eb2', '2160.ek1', '2160.eo1', '3240.ep1', '3240.fe1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [462320225425, 7185162389, 19678982548, 80880, 80787], 'label': '77760.bo.1080.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.ez1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ez1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055352
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.eg1', '540.m1', '540.cd1', '540.dt1', '540.ek1', '540.ha1'], 'contains': ['2160.eb2', '2160.el1', '2160.ep1', '3240.eq1', '3240.ff1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [7185029309, 19678982548, 462320328958, 80880, 80787], 'label': '77760.bo.1080.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.fa1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.fa1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055353
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.eh1', '540.m1', '540.ce1', '540.ds1', '540.ep1', '540.gq1'], 'contains': ['2160.eb2', '2160.en1', '2160.eq1', '3240.er1', '3240.fg1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [462320225425, 19678982548, 80880, 80787, 7185202680], 'label': '77760.bo.1080.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.fb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.fb1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055354
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.ce2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.bw1', '360.ej1', '540.r1', '540.cg1', '540.du1', '540.el1', '540.ge1', '540.gj1', '540.hf1'], 'contains': ['2160.eb1', '2160.ek1', '3240.es1', '3240.fo1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [83601118, 456053207518, 87262035388, 143975, 80787], 'label': '77760.bo.1080.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.fc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.fc1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246055355
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.dz1', '540.bj1', '540.bz1', '540.cz2', '540.eo1', '540.gf1', '540.gg1', '540.hd1'], 'contains': ['2160.ec2', '2160.ed1', '2160.ef1', '2160.ge1', '2160.ge2', '3240.et1', '3240.ev1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [448908278999, 19678982548, 80880, 80787, 462320046985], 'label': '77760.bo.1080.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.fd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.fd1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055356
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.fd2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.dz2', '540.bj1', '540.bz2', '540.cz1', '540.em1', '540.gi1', '540.gk1', '540.gv1'], 'contains': ['2160.ec1', '2160.ed2', '2160.ef1', '2160.ge1', '2160.ge2', '3240.et2', '3240.ev2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [462320230444, 19678982548, 461841188401, 80880, 80787], 'label': '77760.bo.1080.fd2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.fd2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.fd2', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055357
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bx1', '360.ea1', '540.bb1', '540.by1', '540.da1', '540.en1', '540.gh1', '540.gv1', '540.hd1'], 'contains': ['2160.ec1', '2160.ed1', '2160.em1', '3240.eu1', '3240.ew1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [83543730, 87262035388, 456053154955, 143975, 80787], 'label': '77760.bo.1080.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.fe1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.fe1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246055358
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ec1', '540.bg1', '540.bx1', '540.dr1', '540.ep1', '540.er1', '540.gk1', '540.hd1'], 'contains': ['2160.ec1', '2160.ef1', '2160.eq1', '3240.ex1', '3240.ez1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [482768881, 375138172205, 80880, 80787, 87182000787], 'label': '77760.bo.1080.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.ff1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ff1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246055359
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.eb1', '540.ba1', '540.ca1', '540.dr1', '540.es1', '540.ew1', '540.gh1', '540.gi1'], 'contains': ['2160.ec1', '2160.eg1', '2160.ej1', '3240.ey1', '3240.fa1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [482635561, 375138172205, 80880, 80787, 87182000787], 'label': '77760.bo.1080.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '1080.fg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.fg1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246055360
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.d1', '20.c1', '30.e1'], 'contains': ['120.n1', '120.o1', '120.bv1', '120.bw1', '120.ca1', '180.m1', '180.n1', '540.cg1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [180587277504, 456053074316, 93448857748, 83543730, 174400173363, 85805, 80880, 80787], 'label': '77760.bo.60.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '60.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.k1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246055361
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ed1', '540.ba1', '540.bx1', '540.dx1', '540.em1', '540.en1', '540.gl1', '540.he1'], 'contains': ['2160.ec1', '2160.eh1', '2160.eo1', '3240.fb1', '3240.fc1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [482808988, 143975, 87182201788, 375138172555, 80787], 'label': '77760.bo.1080.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.fh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.fh1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246055362
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.ee1', '540.y1', '540.bv1', '540.ds1', '540.ew1', '540.gg1'], 'contains': ['2160.ec2', '2160.ej1', '2160.en1', '3240.fd1', '3240.fh1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [7185024000, 19679028004, 143975, 462320328958, 80787], 'label': '77760.bo.1080.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '1080.fi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.fi1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246055363
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.ef1', '540.z1', '540.bv1', '540.dt1', '540.fa1', '540.gf1', '540.gj1', '540.hg1'], 'contains': ['2160.ec2', '2160.ek1', '2160.ep1', '3240.fe1', '3240.fi1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [7185207845, 19679028004, 143975, 462320328958, 80787], 'label': '77760.bo.1080.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '1080.fj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.fj1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246055364
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.eg1', '540.y1', '540.bw1', '540.dt1', '540.eo1', '540.he1'], 'contains': ['2160.ec2', '2160.el1', '2160.eo1', '3240.ff1', '3240.fj1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [7185029309, 19679028004, 143975, 462320328958, 80787], 'label': '77760.bo.1080.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.fk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.fk1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055365
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.eh1', '540.z1', '540.bw1', '540.ds1', '540.eq1', '540.hd1'], 'contains': ['2160.ec2', '2160.em1', '2160.eq1', '3240.fg1', '3240.fk1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [19679028004, 143975, 462320328958, 80787, 7185202680], 'label': '77760.bo.1080.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.fl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.fl1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055366
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ei1', '540.p1', '540.bz2', '540.ea1', '540.ep1', '540.gh1', '540.gl1', '540.ha1'], 'contains': ['2160.eb2', '2160.ec1', '2160.eh1', '2160.gi1', '2160.gi2', '3240.fl1', '3240.fn1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [19679345155, 80880, 80787, 448908283914, 462320046985], 'label': '77760.bo.1080.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.fm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.fm1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055367
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.fm2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ei1', '540.p2', '540.bz1', '540.ea1', '540.eq1', '540.gg1', '540.gj1', '540.he1'], 'contains': ['2160.eb1', '2160.ec2', '2160.eh1', '2160.gi1', '2160.gi2', '3240.fl2', '3240.fn1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [19679028004, 143975, 461841148348, 462320328958, 80787], 'label': '77760.bo.1080.fm2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.fm2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.fm2', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055368
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.by1', '360.ek1', '540.o1', '540.by1', '540.du1', '540.er1', '540.gi1', '540.ha1', '540.he1'], 'contains': ['2160.eb1', '2160.ec1', '2160.el1', '3240.fm1', '3240.fp1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [83601118, 87262035388, 456053154955, 143975, 80787], 'label': '77760.bo.1080.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.fn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.fn1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246055369
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.bz1', '360.ej1', '540.bb1', '540.cb1', '540.du1', '540.es1', '540.gk1', '540.gl1', '540.hg1'], 'contains': ['2160.ec1', '2160.ek1', '3240.fo1', '3240.fq1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [83548555, 87262035388, 456053154955, 143975, 80787], 'label': '77760.bo.1080.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '1080.fo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.fo1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246055370
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.el1', '540.bg1', '540.cf1', '540.db1', '540.ei1', '540.ek1', '540.gf1', '540.gv1'], 'contains': ['2160.ed1', '2160.ef1', '2160.ep1', '3240.fr1', '3240.fx1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [482635916, 375138087093, 80880, 80787, 87182000787], 'label': '77760.bo.1080.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.fp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.fp1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246055371
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.a1', '30.c1', '30.d1', '30.h1'], 'contains': ['120.m1', '120.bt1', '120.cc1', '180.o1', '180.br1', '180.bs1', '240.i1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [262972155121, 374659361282, 87182277125, 143975, 355938110909, 85805, 80880, 80787], 'label': '77760.bo.60.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '60.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.l1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246055372
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.el1', '540.ba1', '540.ci1', '540.db1', '540.en1', '540.eo1', '540.gd1', '540.gn1'], 'contains': ['2160.ed1', '2160.eg1', '2160.eo1', '3240.fr1', '3240.fy1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [482849425, 375138087093, 143975, 87182201788, 80787], 'label': '77760.bo.1080.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.fq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.fq1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246055373
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.em1', '540.ba1', '540.cf1', '540.df1', '540.et1', '540.ex1', '540.gg1', '540.gh1'], 'contains': ['2160.ed1', '2160.eh1', '2160.ej1', '3240.fs1', '3240.fz1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [180667289547, 442641386755, 443120250115, 143975, 80787], 'label': '77760.bo.1080.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.fr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.fr1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246055374
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.em1', '540.dg1', '540.eu1', '540.ey1'], 'contains': ['2160.ee1', '2160.ei1', '2160.er1', '3240.fs1', '3240.ga1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [482808988, 87182201544, 375138087093, 80787, 179159], 'label': '77760.bo.1080.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '1080.fs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.fs1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055375
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.en1', '540.y1', '540.cd1', '540.dc1', '540.ex1', '540.gi1'], 'contains': ['2160.ed2', '2160.ej1', '2160.el1', '3240.ft1', '3240.gb1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [7185104880, 462320323891, 19678982548, 80880, 80787], 'label': '77760.bo.1080.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.ft1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ft1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055376
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.eo1', '540.z1', '540.ce1', '540.dc1', '540.fb1', '540.ge1', '540.gk1', '540.hh1'], 'contains': ['2160.ed2', '2160.ek1', '2160.eq1', '3240.fu1', '3240.gc1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [462320323652, 19679028004, 143975, 80787, 7185202680], 'label': '77760.bo.1080.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.fu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.fu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055377
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.ep1', '540.z1', '540.cd1', '540.dd1', '540.ej1', '540.gv1'], 'contains': ['2160.ed2', '2160.em1', '2160.ep1', '3240.fv1', '3240.gd1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [7185029309, 462320323891, 19678982548, 80880, 80787], 'label': '77760.bo.1080.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.fv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.fv1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055378
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.ep1', '540.y1', '540.ce1', '540.dd1', '540.em1', '540.gn1'], 'contains': ['2160.ed2', '2160.en1', '2160.eo1', '3240.fv1', '3240.ge1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [7185029309, 462320323652, 19679028004, 143975, 80787], 'label': '77760.bo.1080.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.fw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.fw1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055379
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.en1', '540.de1', '540.ey1'], 'contains': ['2160.ee2', '2160.er1', '2160.et1', '3240.ft1', '3240.gf1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [462320323891, 7185024000, 19679028004, 80787, 179159], 'label': '77760.bo.1080.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '1080.fx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.fx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055380
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.eo1', '540.de1', '540.fc1', '540.hi1'], 'contains': ['2160.ee2', '2160.es1', '2160.eu1', '3240.fu1', '3240.gg1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [462320323891, 19679028004, 80787, 7185202680, 179159], 'label': '77760.bo.1080.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '1080.fy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.fy1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055381
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.ca1', '360.eq1', '540.bb1', '540.cg1', '540.dh1', '540.et1', '540.gd1', '540.gf1', '540.hh1'], 'contains': ['2160.ed1', '2160.ek1', '3240.fw1', '3240.gh1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [83543730, 87262035388, 143975, 456053150130, 80787], 'label': '77760.bo.1080.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.fz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.fz1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246055382
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['20.d1', '30.e1'], 'contains': ['120.a1', '120.b1', '120.c1', '120.h1', '120.k1', '120.n1', '120.q1', '120.r1', '120.v1', '120.w1', '120.y1', '180.p1', '180.r1', '180.bt1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [180587277504, 456053074316, 93448857748, 174400173363, 85805, 80880, 80787, 693], 'label': '77760.bo.60.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '60.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.m1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246055383
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.cb1', '360.eq1', '540.di1', '540.eu1', '540.hi1'], 'contains': ['2160.ee1', '2160.es1', '3240.fw1', '3240.gi1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [83543730, 87262035144, 456053150130, 80787, 179159], 'label': '77760.bo.1080.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '1080.ga1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ga1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055384
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.er1', '540.bl1', '540.ch1', '540.eb1', '540.ei1', '540.em1', '540.ep1', '540.gg1'], 'contains': ['2160.ef1', '2160.eh1', '2160.en1', '3240.gj1', '3240.gl1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87182277125, 355938248904, 143975, 374659446987, 80787], 'label': '77760.bo.1080.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.gb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.gb1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246055385
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.ce2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.es1', '540.bo1', '540.ch1', '540.dv1', '540.el1', '540.ez1', '540.gf1', '540.gk1'], 'contains': ['2160.ef1', '2160.ek1', '3240.gk1', '3240.go1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [355938463434, 87182277597, 374659084948, 80880, 80787], 'label': '77760.bo.1080.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.gc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.gc1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246055386
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.er1', '540.bc1', '540.ck1', '540.eb1', '540.ej1', '540.en1', '540.eq1', '540.gh1'], 'contains': ['2160.eg1', '2160.eh1', '2160.em1', '3240.gl1', '3240.gm1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [355938284280, 87181925066, 374659084948, 80880, 80787], 'label': '77760.bo.1080.gd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.gd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.gd1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246055387
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.et1', '540.bl1', '540.ck1', '540.dv1', '540.ek1', '540.eo1', '540.er1', '540.gi1'], 'contains': ['2160.ef1', '2160.eg1', '2160.el1', '3240.gn1', '3240.gp1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [355938289445, 87182277125, 143975, 374659446987, 80787], 'label': '77760.bo.1080.ge1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.ge1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ge1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246055388
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.es1', '540.bc1', '540.cl1', '540.dv1', '540.es1', '540.fa1', '540.gd1', '540.ge1'], 'contains': ['2160.eg1', '2160.ek1', '3240.go1', '3240.gq1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [355938289445, 87182277597, 143975, 374659446987, 80787], 'label': '77760.bo.1080.gf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '1080.gf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.gf1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246055389
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.eu1', '540.bc1', '540.ch1', '540.ee1', '540.et1', '540.fb1', '540.gj1', '540.gl1'], 'contains': ['2160.eh1', '2160.ek1', '3240.gr1', '3240.gs1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [87182202116, 355938387815, 374659084948, 80880, 80787], 'label': '77760.bo.1080.gg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.gg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.gg1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246055390
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.eu1', '540.ef1', '540.eu1', '540.fc1'], 'contains': ['2160.ei1', '2160.es1', '3240.gr1', '3240.gt1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [355938284280, 374659447084, 87182202116, 80787, 179159], 'label': '77760.bo.1080.gh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '1080.gh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.gh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055391
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ev1', '540.a1', '540.bd1', '540.dw1', '540.fs1', '540.gm1', '540.gz1', '540.hj1'], 'contains': ['2160.fg1', '3240.gv1', '3240.gw1', '3240.gx1', '4320.bn1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [355462732800, 375138305854, 143975, 87660962185, 462320328386], 'label': '77760.bo.1080.gi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '1080.gi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.gi1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246055392
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.ce2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ew1', '360.ex1', '360.ey1', '540.q1', '540.ci1', '540.dx1', '540.fd1', '540.gn1', '540.he1', '540.hf1'], 'contains': ['2160.eb1', '2160.eo1', '2160.fb1', '3240.gu1', '3240.gy1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [482711044, 375138172555, 80880, 80787, 87182000787], 'label': '77760.bo.1080.gj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.gj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.gj1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246055393
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.c1', '12.d1', '12.n1', '18.b1', '18.f1', '36.d1', '60.c1', '90.d1'], 'core': '12.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [93924369357, 143975, 462320328958, 85805, 80787], 'label': '77760.bo.6.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1', 'subgroup_fusion': None, 'weyl_group': '25920.w'}
  • id: 246055394
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.e1', '20.e1', '30.e1'], 'contains': ['120.d1', '120.e1', '120.o1', '120.p1', '120.r1', '120.z1', '120.ba1', '180.q1', '180.s1', '540.co1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [80787, 482768881, 143304, 280259521949, 88695348625, 85805, 80880, 193999455627], 'label': '77760.bo.60.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '60.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.n1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246055395
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.s1', '360.ew1', '540.b1', '540.be1', '540.dy1', '540.fe1', '540.go1', '540.gy1', '540.hj1'], 'contains': ['2160.fg1', '3240.gu1', '3240.ha1', '4320.br1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [148, 375138172555, 188331091348, 87181920000, 482630643], 'label': '77760.bo.1080.gk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '1080.gk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.gk1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246055396
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ew1', '540.dz1', '540.ff1', '540.gp1'], 'contains': ['2160.fh1', '3240.gu1', '3240.hb1', '4320.bt1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [179012, 443120204612, 442641300482, 442162103187, 180667065600], 'label': '77760.bo.1080.gl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bu1', 'old_label': '1080.gl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.gl1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246055397
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.ec1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ev1', '360.fb1', '540.s1', '540.cj1', '540.ea1', '540.ev1', '540.gq1', '540.ha1', '540.hf1'], 'contains': ['2160.eb1', '2160.eb2', '2160.fb1', '3240.gv1', '3240.hd1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [19678982548, 462320328958, 80880, 80787, 448908283914], 'label': '77760.bo.1080.gm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '1080.gm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.gm1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055398
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ev1', '360.ez1', '540.t1', '540.bf1', '540.cu1', '540.ft1', '540.gr1', '540.hb1', '540.hk1'], 'contains': ['2160.fd1', '3240.gw1', '3240.hd1', '4320.bp1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [19679028004, 461841050404, 462320328958, 262496586387, 80787], 'label': '77760.bo.1080.gn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '1080.gn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.gn1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246055399
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ev1', '360.fa1', '540.u1', '540.gs1', '540.hc1'], 'contains': ['2160.fe1', '3240.gx1', '3240.hd1', '4320.bq1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [87661279197, 355462813680, 375138363450, 462320328958, 80787], 'label': '77760.bo.1080.go1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1', 'old_label': '1080.go1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.go1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246055400
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ez1', '540.e1', '540.v1', '540.dw1', '540.fu1', '540.gt1', '540.gy1', '540.hl1'], 'contains': ['2160.fg1', '3240.gw1', '3240.he1', '4320.bs1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841004800, 262496649575, 19678982400, 143975, 462320328958], 'label': '77760.bo.1080.gp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '1080.gp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.gp1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246055401
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ey1', '360.fc1', '540.bg1', '540.ca1', '540.dx1', '540.fg1', '540.gv1', '540.ha1', '540.hg1'], 'contains': ['2160.ec1', '2160.ep1', '2160.fb1', '3240.gy1', '3240.gz1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [482676004, 143975, 87182201788, 375138172555, 80787], 'label': '77760.bo.1080.gq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '1080.gq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.gq1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246055402
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.t1', '360.ew1', '360.fc1', '540.w1', '540.bh1', '540.cv1', '540.fh1', '540.gu1', '540.hb1', '540.hk1'], 'contains': ['2160.fd1', '3240.gy1', '3240.ha1', '3240.hb1', '4320.ca1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [188331171987, 482676004, 375138172555, 80787, 87182000787], 'label': '77760.bo.1080.gr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '1080.gr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.gr1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246055403
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.gs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ex1', '360.fc1', '540.bi1', '540.fi1', '540.hc1'], 'contains': ['2160.fe1', '3240.gy1', '3240.hc1', '4320.cb1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [482676004, 188331136563, 375138172205, 80787, 87182000787], 'label': '77760.bo.1080.gs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.k1', 'old_label': '1080.gs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.gs1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
  • id: 246055404
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.gt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.u1', '360.fc1', '540.f1', '540.x1', '540.dy1', '540.fj1', '540.gw1', '540.gz1', '540.hl1'], 'contains': ['2160.fg1', '3240.gz1', '3240.ha1', '3240.hc1', '4320.cc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [482711044, 45363, 188331136563, 375138172205, 87181920000], 'label': '77760.bo.1080.gt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '1080.gt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.gt1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246055405
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.f1', '15.a1', '20.d1'], 'contains': ['120.f1', '120.i1', '120.j1', '120.l1', '120.s1', '120.t1', '120.u1', '120.bc1', '120.bd1', '120.be1', '120.bf1', '180.bt1', '180.bv1'], 'core': '720.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [143975, 80787, 519235320, 143304, 85805, 442641386424, 998144375, 80880], 'label': '77760.bo.60.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '60.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.o1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246055406
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.gu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fc1', '540.dz1', '540.fk1', '540.gx1'], 'contains': ['2160.fh1', '3240.gz1', '3240.hb1', '3240.hc1', '4320.cd1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [443120025600, 180667065843, 442641109705, 442162067904, 148], 'label': '77760.bo.1080.gu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bu1', 'old_label': '1080.gu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.gu1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246055407
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.gv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ez1', '360.fa1', '360.fb1', '540.bj1', '540.cc1', '540.ea1', '540.ew1', '540.hd1', '540.he1', '540.hg1'], 'contains': ['2160.ec1', '2160.ec2', '2160.fb1', '3240.hd1', '3240.he1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [19679028004, 143975, 448908284158, 462320328958, 80787], 'label': '77760.bo.1080.gv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '1080.gv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.gv1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246055408
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.gw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.fd1', '360.fe1', '540.bf1', '540.cq1', '540.fv1', '540.gu1', '540.hm1'], 'contains': ['2160.fd1', '3240.hg1', '3240.hh1', '3240.hi1', '4320.ce1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [462320323891, 19679028004, 461841050404, 262496586387, 80787], 'label': '77760.bo.1080.gw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '1080.gw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.gw1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246055409
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.gx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ff1', '360.fg1', '360.fh1', '540.bg1', '540.ci1', '540.df1', '540.fl1', '540.gq1', '540.hd1', '540.hh1'], 'contains': ['2160.ed1', '2160.eq1', '2160.fb1', '3240.hf1', '3240.hj1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [482676004, 375138087093, 143975, 87182201788, 80787], 'label': '77760.bo.1080.gx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.gx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.gx1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246055410
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.gy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.fh1', '360.fi1', '360.fj1', '540.dg1', '540.fm1', '540.hi1'], 'contains': ['2160.ee1', '2160.eu1', '2160.fc1', '3240.hf1', '3240.hk1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [443120204759, 180667146387, 442641386755, 80787, 179159], 'label': '77760.bo.1080.gy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '1080.gy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.gy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055411
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.gz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.v1', '360.ff1', '360.fi1', '540.bh1', '540.cr1', '540.fn1', '540.gr1', '540.hm1'], 'contains': ['2160.fd1', '3240.hf1', '3240.hl1', '4320.ch1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [188331171987, 482676004, 375138087093, 80787, 87182000787], 'label': '77760.bo.1080.gz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '1080.gz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.gz1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246055412
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ha1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ff1', '360.fg1', '360.fj1', '540.bi1', '540.fo1', '540.gs1'], 'contains': ['2160.fe1', '3240.hf1', '3240.hm1', '4320.ci1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [188331270212, 482676004, 375138087093, 80787, 87182000787], 'label': '77760.bo.1080.ha1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.l1', 'old_label': '1080.ha1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ha1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246055413
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.hb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.fg1', '360.fi1', '360.fj1', '540.fp1'], 'contains': ['2160.ff1', '3240.hf1', '3240.hn1', '4320.cj1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [443120071204, 180667146387, 442641386755, 80787, 442162201559], 'label': '77760.bo.1080.hb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.fp1', 'old_label': '1080.hb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.hb1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055414
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.hc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fd1', '360.fk1', '540.bj1', '540.cj1', '540.dj1', '540.ex1', '540.gn1', '540.gv1', '540.hh1'], 'contains': ['2160.ed1', '2160.ed2', '2160.fb1', '3240.hg1', '3240.ho1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841004948, 462320323891, 19678982548, 80880, 80787], 'label': '77760.bo.1080.hc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '1080.hc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.hc1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055415
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.hd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.fe1', '360.fk1', '540.dk1', '540.ey1', '540.hi1'], 'contains': ['2160.ee1', '2160.ee2', '2160.fc1', '3240.hg1', '3240.hp1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [462320323891, 19679028004, 461841050404, 80787, 179159], 'label': '77760.bo.1080.hd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '1080.hd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.hd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055416
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.g1', '30.f1', '30.g1', '30.h1'], 'contains': ['120.m1', '120.bg1', '180.bu1', '180.by1', '240.s1'], 'core': '720.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [355499159518, 355419504452, 143975, 442681079189, 85805, 80880, 80787, 143304], 'label': '77760.bo.60.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '60.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.p1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246055417
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.he1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fd1', '540.e1', '540.bd1', '540.dl1', '540.fw1', '540.go1', '540.gw1', '540.hn1'], 'contains': ['2160.fg1', '3240.hh1', '3240.ho1', '4320.ck1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [355462732800, 87661064904, 375138087093, 143975, 462320369015], 'label': '77760.bo.1080.he1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '1080.he1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.he1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246055418
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.hf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fd1', '540.dm1', '540.gp1', '540.gx1'], 'contains': ['2160.fh1', '3240.hi1', '3240.ho1', '4320.cl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [461841004800, 19678982400, 143975, 262496684612, 462320369015], 'label': '77760.bo.1080.hf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.z1', 'old_label': '1080.hf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.hf1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246055419
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.hg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.fe1', '540.dn1', '540.fx1', '540.ho1'], 'contains': ['2160.fi1', '3240.hh1', '3240.hp1', '4320.cm1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [355462732800, 87661100280, 375138086998, 462320369015, 179159], 'label': '77760.bo.1080.hg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '1080.hg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.hg1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246055420
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.hh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.fe1', '540.do1'], 'contains': ['2160.fj1', '3240.hi1', '3240.hp1', '4320.cn1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [461841004800, 262496649331, 19678982400, 462320369015, 179159], 'label': '77760.bo.1080.hh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.cd1', 'old_label': '1080.hh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.hh1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 246055421
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.hi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.w1', '360.ff1', '540.f1', '540.be1', '540.dp1', '540.fq1', '540.gm1', '540.gt1', '540.hn1'], 'contains': ['2160.fg1', '3240.hj1', '3240.hl1', '3240.hm1', '4320.cu1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [375138087093, 482630400, 143975, 188331091200, 87182282187], 'label': '77760.bo.1080.hi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '1080.hi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.hi1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246055422
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.hj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.x1', '360.fi1', '540.dq1', '540.fr1', '540.ho1'], 'contains': ['2160.fi1', '3240.hk1', '3240.hl1', '3240.hn1', '4320.cv1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [87182237067, 375138087093, 482630400, 188331091200, 224612], 'label': '77760.bo.1080.hj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '1080.hj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.hj1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246055423
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.hk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.ce2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fl1', '360.fm1', '360.fn1', '540.bo1', '540.ck1', '540.eb1', '540.ev1', '540.fd1', '540.gv1', '540.hd1'], 'contains': ['2160.ef1', '2160.em1', '2160.fb1', '3240.hq1', '3240.hr1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87182277597, 355938186480, 374659084948, 80880, 80787], 'label': '77760.bo.1080.hk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.hk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.hk1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246055424
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.hl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fl1', '540.i1', '540.bk1', '540.ec1', '540.fe1', '540.fs1', '540.gt1', '540.gw1'], 'contains': ['2160.fg1', '3240.hq1', '3240.ht1', '4320.cx1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87657333149, 19203891388, 374659366588, 87182201788, 224515], 'label': '77760.bo.1080.hl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '1080.hl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.hl1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246055425
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.hm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fl1', '540.ed1', '540.ff1', '540.gx1'], 'contains': ['2160.fh1', '3240.hq1', '3240.hu1', '4320.cy1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [374659165680, 19203654963, 87657511685, 80880, 87181920000], 'label': '77760.bo.1080.hm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bu1', 'old_label': '1080.hm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.hm1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246055426
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.hn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fn1', '360.fo1', '540.bl1', '540.cl1', '540.eb1', '540.ew1', '540.fg1', '540.gn1', '540.gq1'], 'contains': ['2160.eg1', '2160.en1', '2160.fb1', '3240.hr1', '3240.hs1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [87182277597, 355938105600, 143975, 374659446987, 80787], 'label': '77760.bo.1080.hn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '1080.hn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.hn1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246055427
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['20.f1', '30.e1'], 'contains': ['120.w1', '120.y1', '120.ba1', '120.bj1', '120.bk1', '120.bv1', '120.bx1', '180.bz1', '180.cg1', '540.da1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [180587277504, 93448857748, 83467916, 174400173363, 456053150130, 80880, 80787, 693], 'label': '77760.bo.60.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '60.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.q1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246055428
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ho1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fl1', '360.fo1', '540.bm1', '540.bp1', '540.cw1', '540.fh1', '540.ft1', '540.gr1', '540.gu1'], 'contains': ['2160.fd1', '3240.hr1', '3240.ht1', '3240.hu1', '4320.da1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [87182277597, 374659084800, 355938105600, 262971878400, 80787], 'label': '77760.bo.1080.ho1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '1080.ho1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ho1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246055429
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.hp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fm1', '360.fo1', '540.bn1', '540.fi1', '540.gs1'], 'contains': ['2160.fe1', '3240.hr1', '3240.hv1', '4320.db1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [87657333149, 374659084800, 19203654963, 80787, 87182000787], 'label': '77760.bo.1080.hp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.k1', 'old_label': '1080.hp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.hp1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
  • id: 246055430
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.hq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fo1', '540.g1', '540.bq1', '540.ec1', '540.fj1', '540.fu1', '540.gm1', '540.go1'], 'contains': ['2160.fg1', '3240.hs1', '3240.ht1', '3240.hv1', '4320.dc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [19203690480, 374659165680, 87657333149, 80880, 87181920000], 'label': '77760.bo.1080.hq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '1080.hq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.hq1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246055431
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.hr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fo1', '540.ed1', '540.fk1', '540.gp1'], 'contains': ['2160.fh1', '3240.hs1', '3240.hu1', '3240.hv1', '4320.dd1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [87181925066, 262971959187, 355938105748, 374659084948, 148], 'label': '77760.bo.1080.hr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bu1', 'old_label': '1080.hr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.hr1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246055432
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.hs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fp1', '360.fq1', '360.fr1', '540.bl1', '540.ck1', '540.ee1', '540.ex1', '540.fl1', '540.ha1', '540.he1'], 'contains': ['2160.eh1', '2160.el1', '2160.fb1', '3240.hw1', '3240.hx1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [355938105600, 87182202116, 143975, 374659446987, 80787], 'label': '77760.bo.1080.hs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1080.hs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.hs1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246055433
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ht1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.fr1', '360.fs1', '360.ft1', '540.ef1', '540.ey1', '540.fm1'], 'contains': ['2160.ei1', '2160.et1', '2160.fc1', '3240.hw1', '3240.hy1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [374659447084, 355938105600, 87182202116, 80787, 179159], 'label': '77760.bo.1080.ht1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '1080.ht1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ht1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055434
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.hu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.fp1', '360.fs1', '540.bm1', '540.cy1', '540.fn1', '540.fv1', '540.hb1'], 'contains': ['2160.fd1', '3240.hw1', '3240.hz1', '4320.dk1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [374659084800, 355938105600, 87182202116, 262971878400, 80787], 'label': '77760.bo.1080.hu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '1080.hu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.hu1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246055435
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.hv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fp1', '360.fq1', '360.ft1', '540.bn1', '540.fo1', '540.hc1'], 'contains': ['2160.fe1', '3240.hw1', '3240.ia1', '4320.dl1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [374659084800, 19203654963, 87657516984, 80787, 87182000787], 'label': '77760.bo.1080.hv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.l1', 'old_label': '1080.hv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.hv1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246055436
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.hw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.fq1', '360.fs1', '360.ft1', '540.fp1'], 'contains': ['2160.ff1', '3240.hw1', '3240.ib1', '4320.dm1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [374659084800, 19203926428, 87657516984, 80787, 87182000787], 'label': '77760.bo.1080.hw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.fp1', 'old_label': '1080.hw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.hw1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055437
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.hx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fp1', '540.g1', '540.bk1', '540.eg1', '540.fq1', '540.fw1', '540.gy1', '540.gz1'], 'contains': ['2160.fg1', '3240.hx1', '3240.hz1', '3240.ia1', '4320.dn1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [19203891388, 374659366588, 87182201788, 224515, 87657516984], 'label': '77760.bo.1080.hx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '1080.hx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.hx1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246055438
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.g1', '20.g1', '30.e1'], 'contains': ['120.w1', '120.z1', '120.bl1', '120.bn1', '120.ca1', '180.ca1', '180.ch1', '540.dh1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [174400208787, 93449036612, 224184, 83543730, 143975, 456053150130, 180587232000, 80787], 'label': '77760.bo.60.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '60.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.r1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 246055439
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.hy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.fs1', '540.eh1', '540.fr1', '540.fx1'], 'contains': ['2160.fi1', '3240.hy1', '3240.hz1', '3240.ib1', '4320.do1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [374659447084, 355938105600, 262972240684, 87182282615, 179159], 'label': '77760.bo.1080.hy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '1080.hy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.hy1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246055440
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.hz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.dj2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.fu1', '360.gg1', '540.bo1', '540.cl1', '540.ee1', '540.fy1', '540.hf1', '540.hg1', '540.hh1'], 'contains': ['2160.ek1', '2160.fb1', '3240.ic1', '3240.id1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [355938105600, 143975, 87182201788, 374659446987, 80787], 'label': '77760.bo.1080.hz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '1080.hz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.hz1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246055441
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ia1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.dk2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.fu1', '360.gh1', '540.ef1', '540.fz1', '540.hi1'], 'contains': ['2160.es1', '2160.fc1', '3240.ic1', '3240.ie1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [87182201544, 374659447084, 355938105600, 80787, 179159], 'label': '77760.bo.1080.ia1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bi1', 'old_label': '1080.ia1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ia1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055442
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ib1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fv1', '360.fx1', '360.fy1', '540.c1', '540.h1', '540.cs1'], 'contains': ['2160.fk1', '2160.fl1', '2160.fo1', '9720.bi1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [456053069398, 174400128000, 180587232000, 83467561, 93448857600], 'label': '77760.bo.1080.ib1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.e1', 'old_label': '1080.ib1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ib1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246055443
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ic1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.r1', '360.fw1', '360.ga1', '360.gc1', '540.d1', '540.h1', '540.cx1'], 'contains': ['2160.fk1', '2160.fm1', '9720.br1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [83548555, 456053154955, 174400128000, 180587232000, 93448857600], 'label': '77760.bo.1080.ic1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '1080.ic1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ic1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246055444
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.id1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.fz1', '360.gb1', '540.c1', '540.cx1'], 'contains': ['2160.fk1', '2160.fn1', '9720.bs1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [83548346, 456053154955, 174400128000, 180587232000, 93448857600], 'label': '77760.bo.1080.id1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.e1', 'old_label': '1080.id1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.id1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246055445
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ie1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.s1', '360.gd1', '360.ge1', '360.gf1', '540.h1', '540.ct1'], 'contains': ['2160.fl1', '2160.fm1', '9720.by1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [456053069398, 83462998, 174400128000, 180587232000, 93448857600], 'label': '77760.bo.1080.ie1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '1080.ie1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ie1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246055446
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.if1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.cj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.a1', '360.gg1', '360.gh1', '540.bp1', '540.cy1', '540.ga1', '540.hk1', '540.hm1'], 'contains': ['2160.fd1', '3240.ic1', '3240.if1', '4320.bj1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [87657292800, 374659084800, 19203655204, 80787, 87182000787], 'label': '77760.bo.1080.if1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '1080.if1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.if1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246055447
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ig1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.q1', '360.gg1', '540.i1', '540.bq1', '540.eg1', '540.gb1', '540.hj1', '540.hl1', '540.hn1'], 'contains': ['2160.fg1', '3240.id1', '3240.if1', '4320.bk1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [19203690480, 374659165680, 80880, 87657338304, 87181920000], 'label': '77760.bo.1080.ig1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '1080.ig1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ig1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246055448
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1080.ih1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.r1', '360.gh1', '540.eh1', '540.gc1', '540.ho1'], 'contains': ['2160.fi1', '3240.ie1', '3240.if1', '4320.bl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [87657292800, 87182282284, 374659447084, 19203971884, 179159], 'label': '77760.bo.1080.ih1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '1080.ih1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ih1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246055449
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1', '20.g1'], 'contains': ['120.x1', '120.bb1', '120.bm1', '120.bo1', '120.cb1', '180.ca1', '180.ci1', '540.di1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [174400208787, 93449001331, 178680, 83543730, 456053150130, 180587232000, 80787, 179159], 'label': '77760.bo.60.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.s1', 'old_label': '60.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.s1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246055450
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1215.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['405.a1', '405.b1', '405.c1'], 'contains': ['2430.a1', '2430.b1', '2430.c1', '2430.d1', '2430.e1', '2430.f1', '2430.g1', '2430.h1', '2430.i1', '2430.j1', '2430.k1', '2430.l1', '2430.m1', '2430.n1', '2430.o1', '2430.p1', '2430.q1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1215, 'diagramx': None, 'generators': [19678982400, 462320011709, 5309, 448908284158, 461841010109, 317252], 'label': '77760.bo.1215.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '1215.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1215.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246055451
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1296.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.b1', '432.a1', '648.a1', '648.b1', '648.h1'], 'contains': ['2592.a1', '2592.h1', '2592.j1', '3888.a1', '6480.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [179012, 1037836800, 18764565242, 40442], 'label': '77760.bo.1296.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d1', 'old_label': '1296.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 246055452
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1296.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.b1', '648.h1'], 'contains': ['2592.a1', '2592.l1', '2592.n1', '3888.b1', '6480.k1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1037980104, 143975, 5066, 18764529866], 'label': '77760.bo.1296.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d1', 'old_label': '1296.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.b1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246055453
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1296.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.e1', '432.a1', '432.c1', '648.d1', '648.e1', '648.i1'], 'contains': ['2592.b1', '2592.g1', '2592.k1', '3888.a1', '6480.q1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1037836800, 5309, 80787, 18764565242], 'label': '77760.bo.1296.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '1296.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.c1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246055454
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1296.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.f1', '432.c1', '648.f1', '648.g1', '648.h1'], 'contains': ['2592.c1', '2592.h1', '2592.l1', '3888.a1', '6480.r1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1037836800, 5066, 80880, 18764565242], 'label': '77760.bo.1296.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d1', 'old_label': '1296.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.d1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246055455
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1296.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.d1', '648.h1'], 'contains': ['2592.c1', '2592.j1', '2592.n1', '3888.b1', '6480.u1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1037980104, 5066, 80880, 18764565242], 'label': '77760.bo.1296.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d1', 'old_label': '1296.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.e1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246055456
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1296.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.b1', '432.d1', '648.i1'], 'contains': ['2592.b1', '2592.k1', '2592.m1', '3888.b1', '6480.v1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1037980104, 85805, 18764529866, 80787], 'label': '77760.bo.1296.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.e1', 'old_label': '1296.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.f1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246055459
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1296.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.j1', '432.f1', '432.g1', '648.i1', '648.j1', '648.k1'], 'contains': ['2592.d1', '2592.g1', '2592.m1', '3888.d1', '6480.bc1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1037980104, 18764703627, 80787, 143304], 'label': '77760.bo.1296.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.e1', 'old_label': '1296.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.i1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 246055460
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.i1', '20.h1', '30.e1'], 'contains': ['120.y1', '120.z1', '120.bw1', '120.by1', '120.bz1', '180.cb1', '180.cm1', '540.du1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [143975, 80787, 174400208787, 143304, 83548555, 93449036612, 180587232000, 456053154955], 'label': '77760.bo.60.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '60.t1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.t1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246055461
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1296.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.h1', '648.i1'], 'contains': ['2592.d1', '2592.k1', '3888.e1', '6480.bi1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [18764748747, 178680, 1038020645, 80787], 'label': '77760.bo.1296.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.e1', 'old_label': '1296.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.j1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246055462
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1296.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.n1', '432.f1', '648.h1', '648.m1', '648.n1'], 'contains': ['2592.e1', '2592.h1', '2592.n1', '3888.d1', '6480.bn1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1037980104, 143975, 18764668104, 143304], 'label': '77760.bo.1296.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '1296.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.k1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246055463
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1296.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.o1', '432.g1', '648.o1'], 'contains': ['2592.f1', '2592.i1', '2592.o1', '3888.d1', '6480.bo1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1037980104, 143731, 18764668104, 143304], 'label': '77760.bo.1296.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.m1', 'old_label': '1296.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.l1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246055464
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1296.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.h1', '648.h1'], 'contains': ['2592.e1', '2592.j1', '2592.l1', '3888.e1', '6480.bq1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [179012, 178680, 18764703480, 1038020645], 'label': '77760.bo.1296.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d1', 'old_label': '1296.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.m1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246055465
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1296.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.p1', '432.i1', '432.m1', '648.d1', '648.j1'], 'contains': ['2592.g1', '3888.f1', '6480.cv1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [181146067200, 267841773604, 269202608787, 80787], 'label': '77760.bo.1296.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '1296.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.n1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 246055466
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1296.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.t1', '432.j1', '432.k1', '648.d1', '648.e1', '648.k1'], 'contains': ['2592.g1', '3888.g1', '6480.cz1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [181146153005, 267841773604, 269202608787, 80787], 'label': '77760.bo.1296.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '1296.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.o1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246055467
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1296.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.v1', '432.l1', '432.n1', '648.e1', '648.j1'], 'contains': ['2592.g1', '3888.h1', '6480.da1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [181146067893, 267841773604, 269202608787, 80787], 'label': '77760.bo.1296.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.e1', 'old_label': '1296.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.p1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 246055468
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1296.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.q1', '432.i1', '648.a1', '648.f1', '648.m1'], 'contains': ['2592.h1', '3888.f1', '6480.db1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [181146067200, 267841773504, 269202528000, 80880], 'label': '77760.bo.1296.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '1296.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.q1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 246055469
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1296.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.s1', '432.j1', '648.a1', '648.g1', '648.n1'], 'contains': ['2592.h1', '3888.g1', '6480.dg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [267841728243, 269202528000, 148, 181146153355], 'label': '77760.bo.1296.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d1', 'old_label': '1296.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.r1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 246055470
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1296.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.u1', '432.k1', '648.b1', '648.f1', '648.n1'], 'contains': ['2592.h1', '3888.g1', '6480.dh1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [269202707012, 179012, 267842044920, 181146153355], 'label': '77760.bo.1296.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d1', 'old_label': '1296.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.s1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246055471
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['30.f1', '30.i1', '30.k1'], 'contains': ['120.bg1', '120.bh1', '120.br1', '180.cc1', '180.cd1', '180.cw1', '240.z1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [461841004948, 462320323320, 143975, 19678982548, 80880, 80787, 262496586694, 143304], 'label': '77760.bo.60.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '60.u1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.u1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246055472
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1296.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.w1', '432.l1', '648.b1', '648.g1', '648.m1'], 'contains': ['2592.h1', '3888.h1', '6480.di1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [181146067893, 267841728243, 269202528000, 148], 'label': '77760.bo.1296.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '1296.t1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.t1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246055473
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1296.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.r1', '432.m1', '648.o1'], 'contains': ['2592.i1', '3888.f1', '6480.dj1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [267842090284, 269202707159, 181146246359, 179159], 'label': '77760.bo.1296.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.m1', 'old_label': '1296.u1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.u1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 246055474
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1296.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.x1', '432.n1', '648.o1'], 'contains': ['2592.i1', '3888.h1', '6480.dm1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [181146067893, 267842045067, 269202752612, 224612], 'label': '77760.bo.1296.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.m1', 'old_label': '1296.v1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.v1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246055475
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1296.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.a1', '432.o1', '432.p1', '432.q1', '648.c1', '648.l1', '648.p1', '648.q1', '648.r1'], 'contains': ['6480.ds1', '7776.c1', '12960.v1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [349232083200, 455574067200], 'label': '77760.bo.1296.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '1296.w1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.w1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
  • id: 246055476
    {'ambient': '77760.bo', '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': '108.a1', 'complements': ['54.a1', '54.b1', '54.g1', '54.f1'], 'conjugacy_class_count': 2, 'contained_in': ['288.a1', '480.d1', '720.a1', '720.ba1', '720.bc1', '720.bh1', '720.bk1'], 'contains': ['2880.a1', '4320.a1', '4320.e1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [183845, 143975, 80880, 80787], 'label': '77760.bo.1440.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1440.a1', 'normal_contained_in': ['4.a1', '720.a1'], 'normal_contains': ['2880.a1', '4320.a1'], 'normalizer': '1.a1', 'old_label': '1440.a1', 'projective_image': '77760.bo', 'quotient_action_image': '2.1', 'quotient_action_kernel': '720.763', 'quotient_action_kernel_order': 720, 'quotient_fusion': None, 'short_label': '1440.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055477
    {'ambient': '77760.bo', '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': '36.a1', 'complements': ['54.a1', '54.b1'], 'conjugacy_class_count': 1, 'contained_in': ['288.b1', '480.g1', '720.a1', '720.cj1', '720.ck1', '720.cl1', '720.cm1'], 'contains': ['2880.a1', '4320.l1', '4320.m1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [143975, 80880, 80787, 143304], 'label': '77760.bo.1440.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1440.b1', 'normal_contained_in': ['4.b1', '720.a1'], 'normal_contains': ['2880.a1'], 'normalizer': '1.a1', 'old_label': '1440.b1', 'projective_image': '77760.bo', 'quotient_action_image': '2.1', 'quotient_action_kernel': '720.763', 'quotient_action_kernel_order': 720, 'quotient_fusion': None, 'short_label': '1440.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055478
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['480.a1', '720.b1', '720.c1', '720.d1', '720.e1', '720.w1'], 'contains': ['2880.k1', '4320.b1', '4320.c1', '4320.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [183845, 193999276800, 280259700485, 80880], 'label': '77760.bo.1440.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '1440.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.c1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 246055479
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.bb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.o1', '480.a1', '480.d1', '720.f1', '720.g1', '720.k1', '720.o1', '720.r1', '720.t1', '720.bl1'], 'contains': ['2880.b1', '4320.b1', '4320.e1', '4320.f1', '4320.g1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [143975, 355419504120, 85805, 80787], 'label': '77760.bo.1440.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '1440.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.d1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055480
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['480.a1', '480.b1', '720.h1', '720.p1', '720.u1'], 'contains': ['2880.f1', '4320.c1', '4320.f1', '4320.g1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [193999276948, 183845, 280259700485, 80787], 'label': '77760.bo.1440.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1', 'old_label': '1440.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.e1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055481
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['480.a1', '480.c1', '720.i1', '720.l1', '720.q1', '720.v1', '720.x1'], 'contains': ['2880.h1', '4320.d1', '4320.f1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [40349, 280259521949, 80787, 193999357587], 'label': '77760.bo.1440.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '1440.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.f1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 246055482
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.j1', '30.g1', '30.j1', '30.k1'], 'contains': ['120.bg1', '120.bi1', '120.bs1', '180.ce1', '180.cf1', '180.cu1', '240.ba1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [143975, 80787, 143304, 180667209003, 442641386424, 443120250115, 80880, 442162067904], 'label': '77760.bo.60.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '60.v1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.v1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246055483
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['480.c1', '720.j1', '720.m1', '720.n1', '720.s1', '720.w1'], 'contains': ['2880.k1', '4320.d1', '4320.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [280259521949, 193999276800, 85805, 80880], 'label': '77760.bo.1440.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '1440.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.g1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 246055484
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.bm1', '480.b1', '480.c1', '480.d1', '720.y1', '720.bb1', '720.bd1', '720.be1', '720.bf1', '720.bi1', '720.bl1'], 'contains': ['2880.b1', '4320.a1', '4320.f1', '4320.h1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 80, 'diagramx': None, 'generators': [85805, 194518275844, 80880, 80787], 'label': '77760.bo.1440.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '1440.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.h1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246055485
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.bn1', '480.b1', '480.d1', '720.z1', '720.bg1', '720.bj1'], 'contains': ['2880.c1', '4320.a1', '4320.g1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 160, 'diagramx': None, 'generators': [183845, 194518374451, 143975, 80787], 'label': '77760.bo.1440.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.a1', 'old_label': '1440.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.i1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055486
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.e1', '480.f1', '720.x1', '720.bm1', '720.bn1', '720.bo1', '720.bp1'], 'contains': ['2880.h1', '4320.i1', '4320.j1', '4320.k1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [193999357894, 280259481600, 80787, 693], 'label': '77760.bo.1440.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '1440.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.j1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 246055487
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.z1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ci1', '480.e1', '480.g1', '720.bl1', '720.bq1', '720.bs1', '720.by1', '720.cc1', '720.cf1', '720.cg1'], 'contains': ['2880.b1', '4320.i1', '4320.l1', '4320.n1', '4320.o1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [143975, 194518339175, 80787, 143304], 'label': '77760.bo.1440.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '1440.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.k1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055488
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.cj1', '480.f1', '480.g1', '720.br1', '720.bt1', '720.bz1'], 'contains': ['2880.d1', '4320.i1', '4320.m1', '4320.p1', '4320.q1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [194518419812, 80787, 143304, 179159], 'label': '77760.bo.1440.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.x1', 'old_label': '1440.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.l1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055489
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['480.e1', '720.bu1', '720.cd1', '720.ch1'], 'contains': ['2880.j1', '4320.j1', '4320.n1', '4320.o1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [193999357894, 280259481600, 143975, 143304], 'label': '77760.bo.1440.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.v1', 'old_label': '1440.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.m1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055490
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['480.e1', '720.w1', '720.bv1', '720.ca1', '720.ce1', '720.ci1'], 'contains': ['2880.k1', '4320.k1', '4320.n1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [280259481600, 143975, 193999277493, 143304], 'label': '77760.bo.1440.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '1440.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.n1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 246055491
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['480.f1', '720.bw1'], 'contains': ['2880.l1', '4320.j1', '4320.p1', '4320.q1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [193999357894, 280259562387, 224184, 224612], 'label': '77760.bo.1440.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.u1', 'old_label': '1440.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.o1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055492
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.f1', '720.bx1', '720.cb1'], 'contains': ['2880.m1', '4320.k1', '4320.p1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [280259481600, 224184, 193999277493, 224612], 'label': '77760.bo.1440.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.s1', 'old_label': '1440.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.p1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 246055493
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['30.f1', '30.j1', '30.l1'], 'contains': ['120.bg1', '120.bp1', '180.cj1', '180.dd1', '240.bc1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [143975, 80787, 262496586694, 143304, 19678982548, 80880, 461841004948, 462320328386], 'label': '77760.bo.60.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '60.w1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.w1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246055494
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.q1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.dj1', '480.h1', '480.j1', '720.f1', '720.y1', '720.bq1', '720.cn1', '720.cq1', '720.cr1', '720.dm1'], 'contains': ['2880.b1', '4320.r1', '4320.t1', '4320.u1', '4320.w1', '4320.x1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [518964004, 442641024148, 80880, 80787], 'label': '77760.bo.1440.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '1440.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.q1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055495
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.t1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.dk1', '480.h1', '480.i1', '720.z1', '720.co1', '720.cs1'], 'contains': ['2880.c1', '4320.r1', '4320.u1', '4320.v1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [174436559876, 80880, 80787, 375138086400], 'label': '77760.bo.1440.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.f1', 'old_label': '1440.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.r1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055496
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.ga1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['480.h1', '480.k1', '720.ba1', '720.cj1', '720.cp1', '720.cp2', '720.ct1', '720.ct2', '720.cw1', '720.cw2'], 'contains': ['2880.a1', '4320.r1', '4320.s1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [442641386424, 143975, 80880, 80787], 'label': '77760.bo.1440.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '1440.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.s1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055497
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.dm1', '480.h1', '480.m1', '720.br1', '720.cu1', '720.dn1'], 'contains': ['2880.d1', '4320.s1', '4320.t1', '4320.v1', '4320.y1', '4320.z1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [174436496787, 375138311012, 80787, 179159], 'label': '77760.bo.1440.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.be1', 'old_label': '1440.t1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.t1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055498
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.dn1', '480.h1', '480.l1', '720.cv1'], 'contains': ['2880.e1', '4320.s1', '4320.u1', '4320.v1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [375138311012, 174436416243, 80787, 179159], 'label': '77760.bo.1440.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.bg1', 'old_label': '1440.u1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.u1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 246055499
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.v1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.do1', '480.i1', '480.j1', '480.k1', '720.g1', '720.bb1', '720.bs1', '720.cx1', '720.da1', '720.df1', '720.dm1'], 'contains': ['2880.b1', '4320.r1', '4320.ba1', '4320.bb1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 80, 'diagramx': None, 'generators': [188331171987, 143975, 80787, 375138230375], 'label': '77760.bo.1440.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '1440.v1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.v1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055500
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.dp1', '480.k1', '480.l1', '480.m1', '720.bt1', '720.dg1', '720.dn1'], 'contains': ['2880.d1', '4320.s1', '4320.ba1', '4320.bc1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 80, 'diagramx': None, 'generators': [188331171987, 375138311012, 80787, 179159], 'label': '77760.bo.1440.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.i1', 'old_label': '1440.w1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.w1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055501
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['480.i1', '480.j1', '480.l1', '720.h1', '720.db1', '720.dh1'], 'contains': ['2880.f1', '4320.u1', '4320.ba1', '4320.be1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 160, 'diagramx': None, 'generators': [93448903104, 174400173363, 83462400, 80787], 'label': '77760.bo.1440.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.a1', 'old_label': '1440.x1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.x1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055502
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['480.i1', '480.l1', '480.m1', '720.di1'], 'contains': ['2880.g1', '4320.v1', '4320.ba1', '4320.bf1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 160, 'diagramx': None, 'generators': [456053068800, 174400208787, 93449001331, 80787], 'label': '77760.bo.1440.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '80.k1', 'old_label': '1440.y1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.y1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055503
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '480.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['480.j1', '480.m1', '720.i1', '720.bm1', '720.dc1', '720.dj1', '720.do1'], 'contains': ['2880.h1', '4320.t1', '4320.ba1', '4320.bd1', '4320.bg1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [456053068800, 174400208787, 93448938387, 80787], 'label': '77760.bo.1440.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '1440.z1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.z1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055504
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.a1', '12.m1', '12.n1', '18.e1', '18.f1', '36.h1', '60.k1', '90.q1'], 'core': '12.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [183845, 143975, 93924236159, 80787, 462320328386], 'label': '77760.bo.6.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1', 'subgroup_fusion': None, 'weyl_group': '25920.w'}
  • id: 246055505
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.k1', '30.g1', '30.i1', '30.l1'], 'contains': ['120.bg1', '120.bq1', '180.ck1', '180.dc1', '240.bd1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [482808988, 188331315147, 87182202116, 143975, 375138270474, 80880, 80787, 143304], 'label': '77760.bo.60.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '60.x1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.x1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246055506
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['480.j1', '720.bu1', '720.cy1', '720.dd1'], 'contains': ['2880.j1', '4320.x1', '4320.bb1', '4320.bd1', '4320.be1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [456053114304, 93448857748, 174400208880, 80880], 'label': '77760.bo.1440.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.v1', 'old_label': '1440.ba1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.ba1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055507
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['480.j1', '720.b1', '720.j1', '720.bv1', '720.cz1', '720.de1', '720.dk1', '720.dp1'], 'contains': ['2880.k1', '4320.w1', '4320.bb1', '4320.be1', '4320.bg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [456053069043, 93448857748, 148, 174400128148], 'label': '77760.bo.1440.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '1440.bb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.bb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055508
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['480.m1', '720.bw1'], 'contains': ['2880.l1', '4320.z1', '4320.bc1', '4320.bd1', '4320.bf1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [93449001331, 174400128000, 456053247959, 179159], 'label': '77760.bo.1440.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.u1', 'old_label': '1440.bc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.bc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055509
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['480.m1', '720.bx1', '720.dl1', '720.dq1'], 'contains': ['2880.m1', '4320.y1', '4320.bc1', '4320.bf1', '4320.bg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [174400128000, 83687012, 93449082212, 224612], 'label': '77760.bo.1440.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.x1', 'old_label': '1440.bd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.bd1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055510
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.c1', '480.n1', '720.bc1', '720.ck1', '720.cw1', '720.cw2', '720.dr1', '720.dr2', '720.ds1', '720.ds2', '720.dt1', '720.du1', '720.dv1', '720.dw1', '720.dx1', '720.dy1', '720.dz1', '720.ea1', '720.eh1'], 'contains': ['2880.a1', '4320.bh1', '4320.bi1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [143975, 80880, 80787, 274467916948], 'label': '77760.bo.1440.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '1440.be1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.be1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055511
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['144.i1', '360.gg1', '480.n1', '480.o1', '720.k1', '720.bd1', '720.by1', '720.dm1', '720.eb1', '720.ec1', '720.ed1'], 'contains': ['2880.b1', '4320.bh1', '4320.bj1', '4320.bk1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [113566924800, 143975, 80787, 88176435715], 'label': '77760.bo.1440.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '1440.bf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.bf1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055512
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.j1', '360.gh1', '480.n1', '480.p1', '720.bz1', '720.dn1', '720.ee1'], 'contains': ['2880.d1', '4320.bi1', '4320.bj1', '4320.bl1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [113566924800, 88176390359, 80787, 179159], 'label': '77760.bo.1440.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.be1', 'old_label': '1440.bg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.bg1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055513
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.o1', '480.p1', '720.l1', '720.bn1', '720.do1', '720.el1', '720.en1', '720.eq1', '720.er1', '720.es1'], 'contains': ['2880.h1', '4320.bj1', '4320.bm1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 10, 'diagramx': None, 'generators': [280259481600, 482676004, 80787, 193999357587], 'label': '77760.bo.1440.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '1440.bh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.bh1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246055514
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['480.o1', '720.c1', '720.m1', '720.ca1', '720.dp1', '720.ek1', '720.em1', '720.eo1', '720.et1', '720.eu1', '720.ev1', '720.ew1'], 'contains': ['2880.k1', '4320.bk1', '4320.bm1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [280259481600, 482630400, 143975, 193999420775], 'label': '77760.bo.1440.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '1440.bi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.bi1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246055515
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.p1', '720.cb1', '720.dq1', '720.ep1', '720.ex1', '720.ey1'], 'contains': ['2880.m1', '4320.bl1', '4320.bm1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [280259481600, 193999455959, 482630400, 179159], 'label': '77760.bo.1440.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.s1', 'old_label': '1440.bj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.bj1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246055516
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['30.h1', '30.i1', '30.j1'], 'contains': ['120.bg1', '120.bt1', '180.cl1', '180.de1', '240.be1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [87182277597, 355938186480, 374659447555, 143975, 262972241015, 80880, 80787, 143304], 'label': '77760.bo.60.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '60.y1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.y1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246055517
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.w1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ev1', '480.q1', '480.r1', '480.s1', '720.f1', '720.be1', '720.cc1', '720.cx1', '720.eb1', '720.ez1', '720.fs1'], 'contains': ['2880.b1', '4320.bn1', '4320.bo1', '4320.bp1', '4320.bq1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [174436416243, 375138172555, 80880, 80787], 'label': '77760.bo.1440.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '1440.bk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.bk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055518
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['480.r1', '720.cd1', '720.cy1', '720.fa1'], 'contains': ['2880.j1', '4320.bn1', '4320.bt1', '4320.bu1', '4320.by1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [83601118, 93449036612, 224515, 174400173604], 'label': '77760.bo.1440.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.cb1', 'old_label': '1440.bl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.bl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055519
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['480.r1', '720.b1', '720.n1', '720.ce1', '720.cz1', '720.ek1', '720.fb1', '720.fk1'], 'contains': ['2880.k1', '4320.bn1', '4320.br1', '4320.bw1', '4320.bx1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [456053074316, 93448857748, 148, 174400128148], 'label': '77760.bo.1440.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '1440.bm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.bm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055520
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.bb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ew1', '480.r1', '480.v1', '720.g1', '720.bf1', '720.cf1', '720.cn1', '720.eb1', '720.fc1', '720.fl1'], 'contains': ['2880.b1', '4320.bo1', '4320.br1', '4320.bt1', '4320.ca1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [442641300958, 442162067904, 80880, 80787], 'label': '77760.bo.1440.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '1440.bn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.bn1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055521
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.n1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ez1', '480.s1', '480.u1', '720.o1', '720.y1', '720.cc1', '720.da1', '720.ec1', '720.ff1', '720.fl1'], 'contains': ['2880.b1', '4320.bp1', '4320.bs1', '4320.bz1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [518964004, 442641109705, 80880, 80787], 'label': '77760.bo.1440.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '1440.bo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.bo1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246055522
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ex1', '480.q1', '480.v1', '720.bg1', '720.co1', '720.fm1'], 'contains': ['2880.c1', '4320.bo1', '4320.cb1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [442162246775, 442641300958, 80880, 80787], 'label': '77760.bo.1440.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.g1', 'old_label': '1440.bp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.bp1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055523
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.n1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fa1', '480.s1', '480.t1', '720.z1', '720.fg1', '720.fm1'], 'contains': ['2880.c1', '4320.bq1', '4320.bz1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [174436559876, 375138172205, 80880, 80787], 'label': '77760.bo.1440.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.f1', 'old_label': '1440.bq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.bq1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055524
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gk1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['480.s1', '480.v1', '720.ba1', '720.bh1', '720.cl1', '720.cp1', '720.cp2', '720.dr1', '720.dr2', '720.fh1', '720.fh2', '720.fn1', '720.fn2'], 'contains': ['2880.a1', '4320.bo1', '4320.bz1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [143975, 442641300958, 80880, 80787], 'label': '77760.bo.1440.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '1440.br1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.br1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055525
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['480.q1', '480.u1', '720.p1', '720.db1', '720.fo1'], 'contains': ['2880.f1', '4320.bp1', '4320.bv1', '4320.cb1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [93448857748, 174400173363, 80787, 83467561], 'label': '77760.bo.1440.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.g1', 'old_label': '1440.bs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.bs1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246055526
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['480.r1', '480.t1', '720.h1', '720.fd1', '720.fo1'], 'contains': ['2880.f1', '4320.bq1', '4320.bw1', '4320.by1', '4320.ca1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [83548555, 93448857748, 174400128243, 80787], 'label': '77760.bo.1440.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1', 'old_label': '1440.bt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.bt1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055527
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '30.h1', '30.k1', '30.l1'], 'contains': ['120.bg1', '120.bu1', '120.cc1', '180.cn1', '180.co1', '180.df1', '240.bb1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [355938186480, 87182202116, 374659447555, 143975, 262972241015, 80880, 80787, 143304], 'label': '77760.bo.60.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '60.z1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.z1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246055528
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.n1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['480.r1', '480.u1', '720.i1', '720.q1', '720.bo1', '720.dc1', '720.el1', '720.fe1', '720.fp1'], 'contains': ['2880.h1', '4320.bp1', '4320.bu1', '4320.bx1', '4320.ca1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [174400208787, 93448938387, 80787, 83467561], 'label': '77760.bo.1440.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '1440.bu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.bu1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055529
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['480.q1', '480.t1', '720.fq1'], 'contains': ['2880.i1', '4320.bq1', '4320.cb1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 960, 'diagramx': None, 'generators': [83548555, 174400352612, 93449081975, 80787], 'label': '77760.bo.1440.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.cl1', 'old_label': '1440.bv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.bv1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055530
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['480.u1', '720.cd1', '720.dd1', '720.fi1'], 'contains': ['2880.j1', '4320.bs1', '4320.bu1', '4320.bv1', '4320.cd1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [174400173363, 80880, 83467561, 93448902963], 'label': '77760.bo.1440.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.cb1', 'old_label': '1440.bw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.bw1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055531
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['480.u1', '720.d1', '720.j1', '720.ce1', '720.de1', '720.em1', '720.fj1', '720.fk1'], 'contains': ['2880.k1', '4320.bs1', '4320.bv1', '4320.bx1', '4320.cc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [93449036612, 179012, 456053154955, 174400128000], 'label': '77760.bo.1440.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '1440.bx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.bx1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055532
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fc1', '480.t1', '480.u1', '480.v1', '720.r1', '720.bb1', '720.cf1', '720.cq1', '720.ec1', '720.fr1', '720.fs1'], 'contains': ['2880.b1', '4320.bz1', '4320.ca1', '4320.cb1', '4320.cc1', '4320.cd1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 80, 'diagramx': None, 'generators': [143975, 442162022400, 442641301050, 80787], 'label': '77760.bo.1440.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '1440.by1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.by1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246055533
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.t1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fd1', '480.w1', '480.x1', '480.y1', '720.o1', '720.be1', '720.bq1', '720.df1', '720.ed1', '720.fc1', '720.fr1'], 'contains': ['2880.b1', '4320.ce1', '4320.cf1', '4320.ck1', '4320.cl1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [174436496787, 375138087093, 143975, 80787], 'label': '77760.bo.1440.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '1440.bz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.bz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055534
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.fe1', '480.y1', '480.z1', '480.ba1', '720.br1', '720.dg1', '720.ee1'], 'contains': ['2880.d1', '4320.ce1', '4320.cg1', '4320.cm1', '4320.cn1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [174436496787, 375138087093, 80787, 179159], 'label': '77760.bo.1440.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ce1', 'old_label': '1440.ca1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.ca1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055535
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['480.w1', '480.x1', '480.z1', '720.p1', '720.dh1', '720.fd1'], 'contains': ['2880.f1', '4320.ce1', '4320.ci1', '4320.cp1', '4320.cs1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [93449036612, 83543730, 174400307012, 80787], 'label': '77760.bo.1440.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.i1', 'old_label': '1440.cb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.cb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055536
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['480.w1', '480.z1', '480.ba1', '720.di1'], 'contains': ['2880.g1', '4320.ce1', '4320.cj1', '4320.cq1', '4320.ct1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [174400352612, 93449001331, 83543730, 80787], 'label': '77760.bo.1440.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '720.di1', 'old_label': '1440.cc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.cc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055537
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['480.x1', '480.ba1', '720.q1', '720.bm1', '720.dj1', '720.en1', '720.fe1'], 'contains': ['2880.h1', '4320.ce1', '4320.ch1', '4320.co1', '4320.cr1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [174400208787, 83543730, 93448938387, 80787], 'label': '77760.bo.1440.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.r1', 'old_label': '1440.cd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.cd1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055538
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['30.a1', '30.c1', '30.i1'], 'contains': ['120.bh1', '120.bq1', '120.bt1', '180.dq1', '180.dr1', '180.ds1', '180.dt1', '240.bf1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [143975, 80787, 19678982548, 262496684612, 448908283441, 462320323320, 80880, 461841004948], 'label': '77760.bo.60.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '60.ba1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.ba1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246055539
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.ba1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ff1', '480.x1', '480.bb1', '720.r1', '720.bf1', '720.bs1', '720.cr1', '720.ed1', '720.ez1', '720.ff1'], 'contains': ['2880.b1', '4320.cf1', '4320.ch1', '4320.ci1', '4320.cu1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [442641386755, 442162067904, 80880, 80787], 'label': '77760.bo.1440.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '1440.ce1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.ce1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055540
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.ba1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fg1', '480.w1', '480.bb1', '720.bg1', '720.cs1', '720.fg1'], 'contains': ['2880.c1', '4320.cf1', '4320.ci1', '4320.cj1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [442641386755, 442162246775, 80880, 80787], 'label': '77760.bo.1440.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.g1', 'old_label': '1440.cf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.cf1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055541
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.ga1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['480.y1', '480.bb1', '720.bh1', '720.cj1', '720.ct1', '720.ct2', '720.ds1', '720.ds2', '720.fh1', '720.fh2'], 'contains': ['2880.a1', '4320.cf1', '4320.cg1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [375138087093, 143975, 80880, 80787], 'label': '77760.bo.1440.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '1440.cg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.cg1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055542
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.fi1', '480.ba1', '480.bb1', '720.bt1', '720.cu1', '720.ee1'], 'contains': ['2880.d1', '4320.cg1', '4320.ch1', '4320.cj1', '4320.cv1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [442641386755, 442162022400, 80787, 179159], 'label': '77760.bo.1440.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.x1', 'old_label': '1440.ch1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.ch1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055543
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.fj1', '480.z1', '480.bb1', '720.cv1'], 'contains': ['2880.e1', '4320.cg1', '4320.ci1', '4320.cj1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [442641386755, 442162067904, 80787, 179159], 'label': '77760.bo.1440.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.bo1', 'old_label': '1440.ci1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.ci1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 246055544
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['480.x1', '720.bu1', '720.fa1', '720.fi1'], 'contains': ['2880.j1', '4320.cl1', '4320.co1', '4320.cs1', '4320.cu1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [83462998, 174400208880, 148, 93448902963], 'label': '77760.bo.1440.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.v1', 'old_label': '1440.cj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.cj1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055545
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['480.x1', '720.d1', '720.n1', '720.bv1', '720.dk1', '720.eo1', '720.fb1', '720.fj1'], 'contains': ['2880.k1', '4320.ck1', '4320.cp1', '4320.cr1', '4320.cu1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [93449082115, 456053069398, 174400128000, 224515], 'label': '77760.bo.1440.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '1440.ck1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.ck1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055546
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['480.ba1', '720.bw1'], 'contains': ['2880.l1', '4320.cn1', '4320.co1', '4320.ct1', '4320.cv1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [93449001331, 456053069398, 174400128000, 179159], 'label': '77760.bo.1440.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.u1', 'old_label': '1440.cl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.cl1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055547
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['480.ba1', '720.bx1', '720.dl1', '720.ep1'], 'contains': ['2880.m1', '4320.cm1', '4320.cq1', '4320.cr1', '4320.cv1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [83462998, 174400128000, 93449036759, 179159], 'label': '77760.bo.1440.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.x1', 'old_label': '1440.cm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.cm1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055548
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fl1', '480.bc1', '480.bd1', '480.be1', '720.k1', '720.bi1', '720.cg1', '720.cn1', '720.cx1', '720.ff1', '720.fr1'], 'contains': ['2880.b1', '4320.cw1', '4320.cx1', '4320.cy1', '4320.da1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [368392152811, 442637475987, 80880, 80787], 'label': '77760.bo.1440.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '1440.cn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.cn1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055549
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['30.a1', '30.k1'], 'contains': ['120.bh1', '120.bs1', '120.bu1', '180.du1', '180.dv1', '180.dw1', '180.dx1', '180.dy1', '240.bg1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [448908278999, 461841004948, 462320323320, 143975, 19678982548, 262496684612, 80880, 80787], 'label': '77760.bo.60.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '60.bb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bb1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246055550
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fm1', '480.bc1', '480.be1', '720.bj1', '720.co1', '720.fg1'], 'contains': ['2880.c1', '4320.cw1', '4320.db1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [368392152811, 442637676988, 80880, 80787], 'label': '77760.bo.1440.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ba1', 'old_label': '1440.co1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.co1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055551
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.d1', '480.be1', '720.bc1', '720.bk1', '720.cm1', '720.cp1', '720.cp2', '720.dt1', '720.fh1', '720.fh2', '720.ft1'], 'contains': ['2880.a1', '4320.cw1', '4320.cz1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [143975, 274468002505, 80880, 80787], 'label': '77760.bo.1440.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '1440.cp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.cp1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055552
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['480.bd1', '720.ch1', '720.cy1', '720.fi1'], 'contains': ['2880.j1', '4320.cx1', '4320.cy1', '4320.de1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [280259527104, 482768881, 80880, 193999357587], 'label': '77760.bo.1440.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.cb1', 'old_label': '1440.cq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.cq1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055553
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['480.bd1', '720.c1', '720.s1', '720.ci1', '720.cz1', '720.fj1'], 'contains': ['2880.k1', '4320.cx1', '4320.dg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [193999276800, 280259527104, 482768881, 80880], 'label': '77760.bo.1440.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '1440.cr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.cr1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246055554
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fo1', '480.be1', '480.bf1', '720.t1', '720.bd1', '720.cg1', '720.cq1', '720.da1', '720.ez1', '720.fc1'], 'contains': ['2880.b1', '4320.cz1', '4320.da1', '4320.db1', '4320.dc1', '4320.dd1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [113566924800, 88176252092, 143975, 80787], 'label': '77760.bo.1440.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '1440.cs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.cs1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246055555
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['480.bc1', '480.bf1', '720.u1', '720.db1', '720.fd1'], 'contains': ['2880.f1', '4320.da1', '4320.db1', '4320.df1', '4320.dh1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [482849425, 193999455812, 280259625575, 80787], 'label': '77760.bo.1440.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.g1', 'old_label': '1440.ct1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.ct1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246055556
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['480.bd1', '480.bf1', '720.l1', '720.v1', '720.bp1', '720.dc1', '720.fe1'], 'contains': ['2880.h1', '4320.da1', '4320.de1', '4320.dg1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [280259481600, 482635561, 80787, 193999357587], 'label': '77760.bo.1440.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '1440.cu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.cu1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246055557
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['480.bf1', '720.ch1', '720.dd1', '720.fa1'], 'contains': ['2880.j1', '4320.dc1', '4320.dd1', '4320.de1', '4320.df1', '4320.dh1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [280259481600, 482849425, 143975, 193999455812], 'label': '77760.bo.1440.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.cb1', 'old_label': '1440.cv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.cv1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246055558
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['480.bf1', '720.e1', '720.m1', '720.ci1', '720.de1', '720.fb1'], 'contains': ['2880.k1', '4320.dc1', '4320.df1', '4320.dg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [280259481600, 482849425, 143975, 193999420775], 'label': '77760.bo.1440.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '1440.cw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.cw1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246055559
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fp1', '480.bg1', '480.bh1', '480.bi1', '720.t1', '720.bi1', '720.by1', '720.cr1', '720.df1', '720.fl1', '720.fs1'], 'contains': ['2880.b1', '4320.di1', '4320.dk1', '4320.dl1', '4320.dn1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [88176292437, 113566924800, 143975, 80787], 'label': '77760.bo.1440.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '1440.cx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.cx1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055560
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['30.b1', '30.c1', '30.j1'], 'contains': ['120.bi1', '120.bp1', '120.bt1', '180.dm1', '180.dz1', '180.ea1', '240.bj1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [143975, 80787, 482768881, 375138172555, 87661140722, 462320328958, 355462813680, 80880], 'label': '77760.bo.60.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '60.bc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bc1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246055561
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fq1', '480.bg1', '480.bi1', '720.bj1', '720.cs1', '720.fm1'], 'contains': ['2880.c1', '4320.di1', '4320.dl1', '4320.dm1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [143975, 368392228437, 442637676843, 80787], 'label': '77760.bo.1440.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ba1', 'old_label': '1440.cy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.cy1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055562
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.e1', '480.bi1', '720.bk1', '720.ck1', '720.ct1', '720.ct2', '720.du1', '720.fn1', '720.fn2', '720.ft1'], 'contains': ['2880.a1', '4320.di1', '4320.dj1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [274468060348, 143975, 80880, 80787], 'label': '77760.bo.1440.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '1440.cz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.cz1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055563
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.fs1', '480.bi1', '480.bj1', '480.bk1', '720.bz1', '720.cu1', '720.dg1'], 'contains': ['2880.d1', '4320.dj1', '4320.dk1', '4320.dm1', '4320.do1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [88176292437, 113566924800, 80787, 179159], 'label': '77760.bo.1440.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ce1', 'old_label': '1440.da1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.da1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055564
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.ft1', '480.bi1', '480.bj1', '720.cv1'], 'contains': ['2880.e1', '4320.dj1', '4320.dl1', '4320.dm1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [368392228437, 442637676988, 80787, 179159], 'label': '77760.bo.1440.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '720.cv1', 'old_label': '1440.db1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.db1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 246055565
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['480.bg1', '480.bh1', '480.bj1', '720.u1', '720.dh1', '720.fo1'], 'contains': ['2880.f1', '4320.dk1', '4320.dl1', '4320.dp1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [482808988, 280259625575, 80787, 193999558588], 'label': '77760.bo.1440.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.i1', 'old_label': '1440.dc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.dc1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055566
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['480.bg1', '480.bj1', '480.bk1', '720.di1'], 'contains': ['2880.g1', '4320.dk1', '4320.dm1', '4320.dq1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [482808988, 280259660759, 193999420531, 80787], 'label': '77760.bo.1440.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '720.di1', 'old_label': '1440.dd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.dd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055567
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.bh1', '480.bk1', '720.v1', '720.bn1', '720.dj1', '720.fp1'], 'contains': ['2880.h1', '4320.dk1', '4320.dr1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [482808988, 280259481600, 80787, 193999357587], 'label': '77760.bo.1440.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '1440.de1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.de1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246055568
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['480.bg1', '480.bj1'], 'contains': ['2880.i2', '4320.dl1', '4320.dm1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 2880, 'diagramx': None, 'generators': [482808988, 280259660759, 193999455812, 80787], 'label': '77760.bo.1440.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1440.df1', 'old_label': '1440.df1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.df1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 246055569
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.df2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['480.bg1', '480.bj1', '720.fq1'], 'contains': ['2880.i1', '4320.dl1', '4320.dm1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [482808988, 193999501175, 280259660759, 80787], 'label': '77760.bo.1440.df2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '720.fq1', 'old_label': '1440.df2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.df2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055570
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['480.bh1', '720.e1', '720.s1', '720.ca1', '720.dk1', '720.fk1'], 'contains': ['2880.k1', '4320.dn1', '4320.dp1', '4320.dr1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [482854584, 193999276800, 280259527104, 80880], 'label': '77760.bo.1440.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '1440.dg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.dg1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246055571
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['30.b1', '30.k1'], 'contains': ['120.bi1', '120.br1', '120.bu1', '180.dn1', '180.eb1', '180.ec1', '240.bn1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [143975, 80787, 87661145547, 375138087093, 462320323891, 355462813680, 80880, 482808988], 'label': '77760.bo.60.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '60.bd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bd1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246055572
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1440.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.bk1', '720.cb1', '720.dl1'], 'contains': ['2880.m1', '4320.do1', '4320.dq1', '4320.dr1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [280259481600, 482854584, 193999501412, 224612], 'label': '77760.bo.1440.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.s1', 'old_label': '1440.dh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.dh1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246055573
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.l1', '810.a1', '810.h1', '810.ba1'], 'contains': ['3240.d2', '3240.h1', '3240.i1', '3240.dp1', '3240.dr1', '3240.eo1', '3240.ep1', '4860.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [19679063280, 183845, 462320190245, 7185162389, 80880], 'label': '77760.bo.1620.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246055574
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.m1', '810.d1', '810.ba1'], 'contains': ['3240.d2', '3240.j1', '3240.k1', '3240.dq1', '3240.ds1', '3240.eq1', '3240.er1', '4860.b1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [7185029309, 45363, 462320328958, 322558, 19679027763], 'label': '77760.bo.1620.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055575
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.n1', '810.c1', '810.d1', '810.bb1'], 'contains': ['3240.d1', '3240.k1', '3240.l1', '3240.di1', '3240.dk1', '3240.em1', '3240.en1', '4860.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [86155, 87182006155, 148, 375138172555, 482716346], 'label': '77760.bo.1620.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055576
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.a1', '540.o1', '810.b1', '810.d1', '810.bc1'], 'contains': ['3240.d1', '3240.g1', '3240.j1', '3240.cz1', '3240.de1', '3240.ek1', '3240.fm1', '4860.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [87261753748, 456053074316, 83462998, 148, 5759], 'label': '77760.bo.1620.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.d1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055577
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.p1', '810.a1', '810.d1', '810.bd1'], 'contains': ['3240.a1', '3240.a2', '3240.d2', '3240.g1', '3240.l1', '3240.cs1', '3240.cs3', '3240.cx1', '3240.dc1', '3240.ej1', '3240.fl1', '4860.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [357597, 19679299652, 45363, 448908283914, 462320011466], 'label': '77760.bo.1620.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.e1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055578
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.e2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.p2', '810.b1', '810.c1', '810.bd1'], 'contains': ['3240.a1', '3240.a2', '3240.d1', '3240.g2', '3240.l1', '3240.cs2', '3240.cs4', '3240.cx2', '3240.dc2', '3240.ej2', '3240.fl2', '4860.e2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [357597, 45363, 448908283914, 19679027763, 462320011466], 'label': '77760.bo.1620.e2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.e2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.e2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055579
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.d2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.b1', '540.q1', '810.b1', '810.h1', '810.bb1'], 'contains': ['3240.d1', '3240.h1', '3240.n1', '3240.dg1', '3240.dw1', '3240.el1', '3240.gu1', '4860.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [482716655, 86155, 87182006155, 148, 375138172555], 'label': '77760.bo.1620.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.f1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246055580
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.d2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.b1', '540.r1', '810.c1', '810.h1', '810.bc1'], 'contains': ['3240.d1', '3240.i1', '3240.cv1', '3240.dz1', '3240.es1', '4860.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [87261753748, 456053074316, 83462643, 148, 5759], 'label': '77760.bo.1620.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.g1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246055581
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.a1', '540.s1', '810.d1', '810.h1', '810.bd1'], 'contains': ['3240.d1', '3240.d2', '3240.n1', '3240.cu1', '3240.cu2', '3240.ec1', '3240.gv1', '4860.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841090505, 179012, 19678982400, 462320363665, 85705], 'label': '77760.bo.1620.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '1620.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.h1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055582
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '30.c1', '30.k1'], 'contains': ['120.bh1', '120.bi1', '120.cc1', '180.ed1', '180.ee1', '180.ef1', '240.bq1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [482711044, 462320323320, 355462813680, 143975, 87660966963, 80880, 80787, 375138230375], 'label': '77760.bo.60.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '60.be1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.be1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246055583
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.a1', '540.t1', '540.v1', '810.e1', '810.i1', '810.l1'], 'contains': ['3240.o1', '3240.ee1', '3240.gw1', '4860.h1', '6480.b1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [462320092105, 461841090505, 19678982400, 262496505600, 85705], 'label': '77760.bo.1620.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '1620.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.i1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055584
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.a1', '540.u1', '810.f1'], 'contains': ['3240.p1', '3240.eg1', '3240.gx1', '4860.h1', '6480.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [355462871610, 87660962042, 462320046842, 375138126842, 40442], 'label': '77760.bo.1620.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1', 'old_label': '1620.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.j1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055585
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['324.a1', '540.b1', '540.w1', '540.x1', '810.g1', '810.i1', '810.m1'], 'contains': ['3240.o1', '3240.ei1', '3240.ha1', '4860.f1', '6480.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [443120025600, 442641024000, 180667151546, 442162022400, 85946], 'label': '77760.bo.1620.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '1620.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.k1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055586
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.y1', '810.b1', '810.ba1'], 'contains': ['3240.g2', '3240.h1', '3240.j1', '3240.fh1', '3240.fj1', '3240.gb1', '3240.ge1', '4860.i1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [19679063280, 462320092205, 183845, 7185162389, 80880], 'label': '77760.bo.1620.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.l1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055587
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.z1', '810.c1', '810.j1', '810.ba1'], 'contains': ['3240.g2', '3240.i1', '3240.k1', '3240.fi1', '3240.fk1', '3240.gc1', '3240.gd1', '4860.j1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [19679063280, 462320092205, 183845, 7185029309, 80880], 'label': '77760.bo.1620.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.m1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055588
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.ba1', '810.a1', '810.b1', '810.bb1'], 'contains': ['3240.g1', '3240.h1', '3240.l1', '3240.fa1', '3240.fc1', '3240.fy1', '3240.fz1', '4860.k1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [277050, 482635561, 45363, 375138172205, 87182197050], 'label': '77760.bo.1620.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.n1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055589
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.c1', '540.bb1', '810.a1', '810.j1', '810.bc1'], 'contains': ['3240.g1', '3240.i1', '3240.ew1', '3240.fq1', '3240.gh1', '4860.l1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [87261753748, 83462998, 456053073961, 148, 5759], 'label': '77760.bo.1620.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.o1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055590
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.bc1', '810.a1', '810.c1', '810.be1'], 'contains': ['3240.i1', '3240.l1', '3240.gm1', '3240.gq1', '3240.gs1', '4860.m1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [87182277597, 179012, 355938324625, 374659442065, 85705], 'label': '77760.bo.1620.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.p1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055591
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.e1', '540.bd1', '540.bf1', '810.g1', '810.k1', '810.l1'], 'contains': ['3240.o1', '3240.gw1', '3240.hh1', '4860.o1', '6480.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [462320092205, 183845, 87661007405, 355462916645, 375138172205], 'label': '77760.bo.1620.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '1620.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.q1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055592
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.f1', '540.bg1', '810.d1', '810.j1', '810.bb1'], 'contains': ['3240.g1', '3240.k1', '3240.n1', '3240.ex1', '3240.fx1', '3240.gz1', '3240.hj1', '4860.n1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [277050, 482988094, 45363, 375138172205, 87182197050], 'label': '77760.bo.1620.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.r1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055593
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['30.a1', '30.d1', '30.j1'], 'contains': ['120.bp1', '120.bs1', '120.bt1', '180.el1', '180.eo1', '180.ep1', '180.eq1', '240.ch1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [448908278999, 461841004948, 143975, 19678982548, 462320328958, 262496684612, 80880, 80787], 'label': '77760.bo.60.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '60.bf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bf1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246055594
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['324.b1', '540.f1', '540.be1', '540.bh1', '810.e1', '810.k1', '810.m1'], 'contains': ['3240.o1', '3240.ha1', '3240.hl1', '4860.n1', '6480.i1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [443120025600, 180667423197, 357597, 442162022400, 442641341252], 'label': '77760.bo.1620.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '1620.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.s1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055595
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.f1', '540.bi1', '810.f1'], 'contains': ['3240.p1', '3240.hc1', '3240.hm1', '4860.n1', '6480.j1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [482716205, 85805, 375138172555, 188331235175, 87182005805], 'label': '77760.bo.1620.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.f1', 'old_label': '1620.t1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.t1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055596
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.e1', '540.bj1', '810.b1', '810.j1', '810.bd1'], 'contains': ['3240.g1', '3240.g2', '3240.n1', '3240.ev1', '3240.ev2', '3240.he1', '3240.ho1', '4860.o1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [19678982400, 143975, 40585, 448908284158, 462320328958], 'label': '77760.bo.1620.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '1620.u1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.u1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055597
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.g1', '540.bl1', '810.b1', '810.d1', '810.be1'], 'contains': ['3240.j1', '3240.l1', '3240.n1', '3240.gj1', '3240.gn1', '3240.hs1', '3240.hx1', '4860.p1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [355938243842, 87182277125, 143975, 374659441925, 5066], 'label': '77760.bo.1620.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.v1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.v1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055598
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.g1', '540.bk1', '540.bm1', '810.e1', '810.g1', '810.n1'], 'contains': ['3240.o1', '3240.ht1', '3240.hz1', '4860.p1', '6480.l1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [87182005946, 374659170746, 19203609600, 85946, 87657516984], 'label': '77760.bo.1620.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '1620.w1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.w1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055599
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.g1', '540.bn1', '810.f1'], 'contains': ['3240.p1', '3240.hv1', '3240.ia1', '4860.p1', '6480.m1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [87182277597, 262972235525, 374659089866, 355938110666, 5066], 'label': '77760.bo.1620.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.f1', 'old_label': '1620.x1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.x1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055600
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.d2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.i1', '540.bo1', '810.h1', '810.j1', '810.be1'], 'contains': ['3240.i1', '3240.n1', '3240.gk1', '3240.hq1', '3240.id1', '4860.q1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [87182277125, 143975, 374659441925, 355938110666, 5066], 'label': '77760.bo.1620.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.y1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.y1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246055601
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.d1', '540.i1', '540.bp1', '540.bq1', '810.i1', '810.k1', '810.n1'], 'contains': ['3240.o1', '3240.ht1', '3240.if1', '4860.q1', '6480.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87657292800, 374659170505, 19203609600, 85705, 87182005705], 'label': '77760.bo.1620.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '1620.z1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.z1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055602
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['162.a1', '405.a1', '540.j1', '540.br1', '540.bt1'], 'contains': ['3240.b1', '3240.e1', '3240.f1', '3240.m1', '3240.q1', '3240.r1', '3240.s1', '3240.bq1', '3240.bt1', '3240.bu1', '3240.cb1', '4860.r1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [518918400, 442641024000, 997920000, 85805, 143304], 'label': '77760.bo.1620.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1620.ba1', 'old_label': '1620.ba1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ba1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246055603
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.c1', '540.bs1', '540.bu1', '810.l1', '810.m1', '810.n1'], 'contains': ['3240.o1', '3240.cd1', '4860.u1', '6480.n1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [355499061242, 355419504452, 442681217850, 317252, 40442], 'label': '77760.bo.1620.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '1620.bb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.bb1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055604
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['30.b1', '30.d1', '30.i1'], 'contains': ['120.bq1', '120.br1', '120.bt1', '180.em1', '180.en1', '180.er1', '240.ck1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [143975, 80787, 87661145547, 482768881, 375138087093, 462320323891, 355462813680, 80880], 'label': '77760.bo.60.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '60.bg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bg1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246055605
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.dv1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.l1', '540.bv1', '810.p1', '810.w1', '810.bf1'], 'contains': ['3240.v2', '3240.z1', '3240.ba1', '3240.dm1', '3240.do1', '3240.fd1', '3240.fe1', '4860.a1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [7185029309, 19679028004, 5309, 462320046842, 80787], 'label': '77760.bo.1620.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1620.bc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.bc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055606
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.m1', '540.bw1', '810.v1', '810.bf1'], 'contains': ['3240.v2', '3240.bb1', '3240.bc1', '3240.dn1', '3240.do1', '3240.ff1', '3240.fg1', '4860.b1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [7185029309, 277050, 19679028004, 462320328958, 80787], 'label': '77760.bo.1620.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.bd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.bd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055607
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.bv1', '810.o1', '810.x1', '810.ba1'], 'contains': ['3240.w2', '3240.bd1', '3240.be1', '3240.dp1', '3240.ds1', '3240.fh1', '3240.fi1', '4860.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [183845, 7185207845, 19678982400, 143975, 462320283450], 'label': '77760.bo.1620.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.be1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.be1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055608
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.bw1', '810.u1', '810.ba1'], 'contains': ['3240.w2', '3240.bf1', '3240.bg1', '3240.dq1', '3240.dr1', '3240.fj1', '3240.fk1', '4860.b1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [183845, 7185029309, 179012, 19678982400, 462320328958], 'label': '77760.bo.1620.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.bf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.bf1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055609
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.bx1', '810.s1', '810.u1', '810.bb1'], 'contains': ['3240.w1', '3240.bg1', '3240.bh1', '3240.dg1', '3240.dk1', '3240.ex1', '3240.fc1', '4860.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [138242, 87182242558, 224515, 375138172555, 482716346], 'label': '77760.bo.1620.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.bg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.bg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055610
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.n1', '540.bx1', '810.t1', '810.v1', '810.bg1'], 'contains': ['3240.v1', '3240.bc1', '3240.bi1', '3240.dh1', '3240.dj1', '3240.ez1', '3240.fb1', '4860.c1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [87181925759, 86155, 482635561, 375138172555, 80787], 'label': '77760.bo.1620.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.bh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.bh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055611
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.f1', '540.by1', '810.q1', '810.u1', '810.bc1'], 'contains': ['3240.w1', '3240.x1', '3240.bf1', '3240.cv1', '3240.de1', '3240.ew1', '3240.fm1', '4860.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [138242, 83462998, 87262035388, 456053154955, 224515], 'label': '77760.bo.1620.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.bi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.bi1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055612
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.bz1', '810.o1', '810.u1', '810.bd1'], 'contains': ['3240.t1', '3240.t2', '3240.w2', '3240.x1', '3240.bh1', '3240.cs2', '3240.cs3', '3240.cu1', '3240.dc1', '3240.ev1', '3240.fl2', '4860.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [183845, 19679161080, 179012, 448908284158, 462320328485], 'label': '77760.bo.1620.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.bj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.bj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055613
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.bj2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.bz2', '810.q1', '810.s1', '810.bd1'], 'contains': ['3240.t1', '3240.t2', '3240.w1', '3240.x2', '3240.bh1', '3240.cs1', '3240.cs4', '3240.cu2', '3240.dc2', '3240.ev2', '3240.fl1', '4860.e2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [219025, 19678982400, 143975, 448908284158, 462320328386], 'label': '77760.bo.1620.bj2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.bj2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.bj2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055614
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.g1', '540.o1', '540.by1', '810.r1', '810.v1', '810.bh1'], 'contains': ['3240.v1', '3240.y1', '3240.bb1', '3240.cy1', '3240.db1', '3240.eu1', '3240.fp1', '4860.d1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [86155, 83543730, 456053154955, 87261834387, 80787], 'label': '77760.bo.1620.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.bk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.bk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055615
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.c1', '3.a1'], 'contains': ['12.a1', '12.d1', '12.h1', '18.g1', '18.h1', '36.i1', '60.n1', '90.t1'], 'core': '12.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [87182277597, 274511462400, 143975, 85805, 80787, 143304], 'label': '77760.bo.6.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1', 'subgroup_fusion': None, 'weyl_group': '25920.w'}
  • id: 246055616
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['30.a1', '30.b1', '30.l1'], 'contains': ['120.bp1', '120.bq1', '120.bu1', '180.es1', '180.et1', '180.eu1', '180.ev1', '240.cn1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [143975, 80787, 87660962042, 375138270474, 355462813680, 80880, 482808988, 462320328386], 'label': '77760.bo.60.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '60.bh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bh1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246055617
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.bc1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.p1', '540.bz1', '810.p1', '810.v1', '810.bi1'], 'contains': ['3240.u1', '3240.u2', '3240.v2', '3240.y1', '3240.bi1', '3240.ct1', '3240.ct2', '3240.cw1', '3240.da1', '3240.et1', '3240.fn1', '4860.e1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [277050, 19679345155, 448908284158, 462320046842, 80787], 'label': '77760.bo.1620.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.bl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.bl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055618
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.bl2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.bc1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.p2', '540.bz2', '810.r1', '810.t1', '810.bi1'], 'contains': ['3240.u1', '3240.u2', '3240.v1', '3240.y2', '3240.bi1', '3240.ct1', '3240.ct3', '3240.cw2', '3240.da2', '3240.et2', '3240.fn1', '4860.e2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [277050, 19679028004, 448908284158, 80787, 462320046985], 'label': '77760.bo.1620.bl2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.bl2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.bl2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055619
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.cg2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.q1', '540.w1', '540.ca1', '810.r1', '810.w1', '810.bg1'], 'contains': ['3240.v1', '3240.z1', '3240.bj1', '3240.dh1', '3240.dv1', '3240.ey1', '3240.gy1', '4860.f1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [443120071204, 40349, 442641024000, 180667151546, 80787], 'label': '77760.bo.1620.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1620.bm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.bm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055620
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.x1', '540.ca1', '810.q1', '810.x1', '810.bb1'], 'contains': ['3240.w1', '3240.bd1', '3240.bk1', '3240.di1', '3240.dw1', '3240.fa1', '3240.gz1', '4860.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [183845, 143975, 482814245, 375138172555, 87182197050], 'label': '77760.bo.1620.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.bn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.bn1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055621
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.cg2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.h1', '540.r1', '540.cb1', '810.t1', '810.w1', '810.bh1'], 'contains': ['3240.v1', '3240.ba1', '3240.cy1', '3240.dy1', '3240.fo1', '4860.g1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [40349, 456053073961, 83462400, 87261834387, 80787], 'label': '77760.bo.1620.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1620.bo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.bo1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055622
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.i1', '540.cb1', '810.s1', '810.x1', '810.bc1'], 'contains': ['3240.w1', '3240.be1', '3240.cz1', '3240.dz1', '3240.fq1', '4860.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [183845, 456053154955, 83606375, 143975, 87262115787], 'label': '77760.bo.1620.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.bp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.bp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055623
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.ec1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.s1', '540.t1', '540.u1', '540.cc1', '810.v1', '810.w1', '810.bi1'], 'contains': ['3240.v1', '3240.v2', '3240.bj1', '3240.cw1', '3240.cw2', '3240.eb1', '3240.hd1', '4860.h1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [277050, 19679028004, 448908284158, 462320328958, 80787], 'label': '77760.bo.1620.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '1620.bq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.bq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055624
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.v1', '540.cc1', '810.u1', '810.x1', '810.bd1'], 'contains': ['3240.w1', '3240.w2', '3240.bk1', '3240.cx1', '3240.cx2', '3240.ec1', '3240.he1', '4860.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [19679063280, 462320092205, 448908001949, 85805, 80880], 'label': '77760.bo.1620.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '1620.br1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.br1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055625
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.cd1', '810.q1', '810.ba1'], 'contains': ['3240.x2', '3240.bd1', '3240.bf1', '3240.eo1', '3240.eq1', '3240.gb1', '3240.gd1', '4860.i1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [183845, 7185207845, 462320283121, 19678982400, 143975], 'label': '77760.bo.1620.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.bs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.bs1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055626
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.ce1', '810.s1', '810.y1', '810.ba1'], 'contains': ['3240.x2', '3240.be1', '3240.bg1', '3240.ep1', '3240.er1', '3240.gc1', '3240.ge1', '4860.j1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [183845, 7185029309, 179012, 19678982400, 462320328485], 'label': '77760.bo.1620.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.bt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.bt1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055627
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.d1', '30.c1', '30.d1', '30.l1'], 'contains': ['120.bp1', '120.bq1', '120.cc1', '180.ew1', '180.ey1', '180.ez1', '240.bt1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [143975, 80787, 87660962042, 482711044, 375138270474, 355462813680, 80880, 462320328386], 'label': '77760.bo.60.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '60.bi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bi1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246055628
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.cf1', '810.o1', '810.q1', '810.bb1'], 'contains': ['3240.x1', '3240.bd1', '3240.bh1', '3240.el1', '3240.en1', '3240.fx1', '3240.fz1', '4860.k1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [183845, 482716205, 143975, 375138270474, 87182197050], 'label': '77760.bo.1620.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.bu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.bu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055629
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.m1', '540.cg1', '810.o1', '810.y1', '810.bc1'], 'contains': ['3240.x1', '3240.be1', '3240.ek1', '3240.es1', '3240.gh1', '4860.l1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [456053207518, 138242, 83462998, 87262035388, 224515], 'label': '77760.bo.1620.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.bv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.bv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055630
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.y1', '540.cd1', '810.r1', '810.bf1'], 'contains': ['3240.y2', '3240.z1', '3240.bb1', '3240.fd1', '3240.ff1', '3240.ft1', '3240.fv1', '4860.i1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [183845, 7185207845, 19679028004, 80787, 462320046985], 'label': '77760.bo.1620.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.bw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.bw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055631
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.z1', '540.ce1', '810.t1', '810.z1', '810.bf1'], 'contains': ['3240.y2', '3240.ba1', '3240.bc1', '3240.fe1', '3240.fg1', '3240.fu1', '3240.fv1', '4860.j1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [183845, 7185029309, 19679028004, 462320046842, 80787], 'label': '77760.bo.1620.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.bx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.bx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055632
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.ba1', '540.cf1', '810.p1', '810.r1', '810.bg1'], 'contains': ['3240.y1', '3240.z1', '3240.bi1', '3240.ey1', '3240.fb1', '3240.fr1', '3240.fs1', '4860.k1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [87182277597, 277050, 375138172205, 80787, 482670985], 'label': '77760.bo.1620.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.by1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.by1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055633
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.n1', '540.bb1', '540.cg1', '810.p1', '810.z1', '810.bh1'], 'contains': ['3240.y1', '3240.ba1', '3240.eu1', '3240.fo1', '3240.fw1', '4860.l1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [86155, 83543730, 456053073961, 87261834387, 80787], 'label': '77760.bo.1620.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.bz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.bz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055634
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.ch1', '810.o1', '810.s1', '810.be1'], 'contains': ['3240.be1', '3240.bh1', '3240.gj1', '3240.gk1', '3240.gs1', '4860.m1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [355938382558, 87182277597, 374659170505, 45363, 5066], 'label': '77760.bo.1620.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.ca1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ca1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055828
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.e1', '720.u1', '1080.c1'], 'contains': ['4320.c1', '4320.df1', '4320.dp1', '6480.l1', '6480.m1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [193999501315, 5161, 482849425, 280259701194], 'label': '77760.bo.2160.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.c1', 'old_label': '2160.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.l1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055635
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.bc1', '540.ch1', '810.p1', '810.t1', '810.bj1'], 'contains': ['3240.ba1', '3240.bi1', '3240.gl1', '3240.go1', '3240.gr1', '4860.m1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [87182277597, 374659170505, 5309, 355938382650, 80787], 'label': '77760.bo.1620.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.cb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.cb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055636
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.be1', '540.ci1', '810.u1', '810.y1', '810.bb1'], 'contains': ['3240.x1', '3240.bg1', '3240.bk1', '3240.em1', '3240.fy1', '3240.gu1', '3240.hj1', '4860.n1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [183845, 143975, 375138270474, 482814245, 87182197050], 'label': '77760.bo.1620.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.cc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.cc1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055637
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.bd1', '540.cj1', '810.q1', '810.y1', '810.bd1'], 'contains': ['3240.x1', '3240.x2', '3240.bk1', '3240.ej1', '3240.ej2', '3240.gv1', '3240.ho1', '4860.o1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [45363, 462320363997, 5066, 448908283914, 19679027763], 'label': '77760.bo.1620.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '1620.cd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.cd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055638
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '60.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.e1', '30.d1', '30.k1'], 'contains': ['120.br1', '120.bs1', '120.cc1', '180.ex1', '180.fa1', '180.fb1', '240.bu1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [143975, 80787, 87661145547, 482711044, 375138087093, 462320323891, 355462813680, 80880], 'label': '77760.bo.60.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '60.bj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bj1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246055639
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.bg1', '540.bh1', '540.bi1', '540.ci1', '810.v1', '810.z1', '810.bg1'], 'contains': ['3240.y1', '3240.bc1', '3240.bj1', '3240.ez1', '3240.fr1', '3240.gy1', '3240.hf1', '4860.n1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [87182277597, 277050, 482952958, 375138172205, 80787], 'label': '77760.bo.1620.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.ce1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ce1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055640
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.bc1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.bf1', '540.bj1', '540.cj1', '810.r1', '810.z1', '810.bi1'], 'contains': ['3240.y1', '3240.y2', '3240.bj1', '3240.et1', '3240.et2', '3240.hd1', '3240.hg1', '4860.o1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [183845, 19679028004, 448908001949, 80787, 462320046749], 'label': '77760.bo.1620.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '1620.cf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.cf1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055641
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.bk1', '540.ck1', '810.q1', '810.u1', '810.be1'], 'contains': ['3240.bf1', '3240.bh1', '3240.bk1', '3240.gm1', '3240.gn1', '3240.hq1', '3240.hx1', '4860.p1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [87181925066, 374659125242, 355938324722, 5066, 80880], 'label': '77760.bo.1620.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.cg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.cg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055642
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.bl1', '540.bm1', '540.bn1', '540.ck1', '810.r1', '810.v1', '810.bj1'], 'contains': ['3240.bb1', '3240.bi1', '3240.bj1', '3240.gl1', '3240.gp1', '3240.hr1', '3240.hw1', '4860.p1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [355938289445, 87181925066, 374659170605, 85805, 80787], 'label': '77760.bo.1620.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.ch1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ch1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055643
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.cg2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.bo1', '540.bp1', '540.cl1', '810.w1', '810.z1', '810.bj1'], 'contains': ['3240.ba1', '3240.bj1', '3240.go1', '3240.hr1', '3240.ic1', '4860.q1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [355938191405, 87181925066, 374659170605, 85805, 80787], 'label': '77760.bo.1620.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1620.ci1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ci1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055644
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.bq1', '540.cl1', '810.x1', '810.y1', '810.be1'], 'contains': ['3240.be1', '3240.bk1', '3240.gq1', '3240.hs1', '3240.id1', '4860.q1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [87181925066, 374659125242, 355938146042, 5066, 80880], 'label': '77760.bo.1620.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.cj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.cj1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055645
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.br1', '540.cm1', '810.bb1', '810.bc1', '810.bd1'], 'contains': ['3240.a1', '3240.d1', '3240.g1', '3240.t1', '3240.w1', '3240.x1', '3240.bl1', '3240.bm1', '3240.cf1', '3240.cg1', '3240.ci1', '4860.r1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [442641386187, 443120169575, 143975, 85805, 143304], 'label': '77760.bo.1620.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.ck1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ck1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055646
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ck2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.cm2', '810.ba1', '810.bd1'], 'contains': ['3240.a2', '3240.d2', '3240.g2', '3240.t2', '3240.w2', '3240.x2', '3240.bl1', '3240.bm1', '3240.cf2', '3240.cg2', '3240.ci2', '4860.r2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [442641386187, 143975, 40585, 448908284158, 143304], 'label': '77760.bo.1620.ck2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.ck2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ck2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246055647
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.d1', '540.cn1', '810.ba1', '810.bb1'], 'contains': ['3240.h1', '3240.k1', '3240.bd1', '3240.bg1', '3240.bm1', '3240.ck1', '3240.cn1', '4860.s1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [443120169575, 267845679358, 143975, 40585, 143304], 'label': '77760.bo.1620.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.cl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.cl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055648
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.q1', '540.co1', '810.ba1', '810.bc1', '810.be1'], 'contains': ['3240.i1', '3240.j1', '3240.be1', '3240.bf1', '3240.bm1', '3240.cl1', '3240.cm1', '4860.t1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [40585, 482768881, 80880, 88695348625, 143304], 'label': '77760.bo.1620.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.cm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.cm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055649
    {'ambient': '77760.bo', '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': '1440.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '24.g1', '36.a1', '36.e1', '36.k1', '36.t1', '36.v1'], 'contains': ['216.a1', '432.o1', '720.eq1', '1080.if1'], 'core': '72.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [274511462400, 80787, 87182000787], 'label': '77760.bo.72.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': ['24.a1', '36.a1'], 'normal_contains': ['216.a1', '25920.a1'], 'normalizer': '1.a1', 'old_label': '72.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.a1', 'subgroup_fusion': None, 'weyl_group': '1440.5842'}
  • id: 246055650
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.bs1', '540.cp1', '810.bb1', '810.bd1', '810.be1'], 'contains': ['3240.l1', '3240.n1', '3240.bh1', '3240.bk1', '3240.bm1', '3240.cj1', '3240.cq1', '4860.u1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [274467916800, 268244524800, 143975, 85805, 143304], 'label': '77760.bo.1620.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '1620.cn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.cn1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055651
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.bt1', '540.cm1', '810.bg1', '810.bh1', '810.bi1'], 'contains': ['3240.u1', '3240.v1', '3240.y1', '3240.bn1', '3240.bo1', '3240.bp1', '3240.bs1', '3240.bv1', '4860.r1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [443120071204, 442641024000, 85805, 80787, 143304], 'label': '77760.bo.1620.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.co1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.co1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055652
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.co2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.cm2', '810.bf1', '810.bi1'], 'contains': ['3240.u2', '3240.v2', '3240.y2', '3240.bn1', '3240.bo1', '3240.bp2', '3240.bs2', '3240.bv2', '4860.r2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [362615, 442641024000, 448908284158, 85805, 80787], 'label': '77760.bo.1620.co2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.co2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.co2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246055653
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.y1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.e1', '540.cn1', '810.bf1', '810.bg1'], 'contains': ['3240.z1', '3240.bc1', '3240.bo1', '3240.bx1', '3240.ca1', '4860.s1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [443120071204, 362615, 267845679358, 85805, 80787], 'label': '77760.bo.1620.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.cp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.cp1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055654
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.y1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.s1', '540.co1', '810.bf1', '810.bh1', '810.bj1'], 'contains': ['3240.ba1', '3240.bb1', '3240.bo1', '3240.by1', '3240.bz1', '4860.t1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [482849425, 85805, 80787, 88695348625, 143304], 'label': '77760.bo.1620.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.cq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.cq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055655
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.bu1', '540.cp1', '810.bg1', '810.bi1', '810.bj1'], 'contains': ['3240.bi1', '3240.bj1', '3240.bo1', '3240.bw1', '3240.cc1', '4860.u1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [274467962404, 268244605587, 85805, 80787, 143304], 'label': '77760.bo.1620.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '1620.cr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.cr1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055656
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.cz1', '810.bi1', '810.bk1', '810.bn1'], 'contains': ['3240.bp1', '3240.bp2', '3240.bs2', '3240.bv1', '3240.bw1', '3240.ct2', '3240.ct3', '3240.cw1', '3240.et2', '4860.v1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [461841090505, 178680, 19679028004, 462320052004, 80787], 'label': '77760.bo.1620.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.cs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.cs1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055657
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.cs2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.cz2', '810.bi1', '810.bl1', '810.bm1'], 'contains': ['3240.bp1', '3240.bp2', '3240.bs1', '3240.bv2', '3240.bw1', '3240.ct1', '3240.cw2', '3240.et1', '4860.v2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [461841090505, 178680, 19679028004, 462320046842, 80787], 'label': '77760.bo.1620.cs2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.cs2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.cs2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055658
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.bz1', '540.da1', '810.bh1', '810.bl1', '810.bn1'], 'contains': ['3240.bs1', '3240.bv1', '3240.bz1', '3240.cy1', '3240.eu1', '4860.w1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [83548555, 456053150130, 87261834387, 45813, 80787], 'label': '77760.bo.1620.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.ct1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ct1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055659
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.db1', '810.bg1', '810.bm1', '810.bn1'], 'contains': ['3240.bs1', '3240.bw1', '3240.ca1', '3240.dh1', '3240.fr1', '4860.x1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [443120071204, 442641024000, 180667203842, 80787, 143304], 'label': '77760.bo.1620.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.cu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.cu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055660
    {'ambient': '77760.bo', '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': '25920.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.d1', '24.b1', '36.c1', '36.d1', '36.i1'], 'contains': ['144.i1', '216.b1', '216.e1', '360.o1', '432.a1', '720.k1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [183845, 349232267045, 455574147987, 80880, 80787], 'label': '77760.bo.72.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1', 'subgroup_fusion': None, 'weyl_group': '1440.5849'}
  • id: 246055661
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.cv1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.dc1', '540.de1', '810.bf1', '810.bk1', '810.br1'], 'contains': ['3240.bs2', '3240.bx1', '3240.by1', '3240.dm1', '3240.dn1', '3240.ft1', '3240.fu1', '4860.y1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [178680, 19679028004, 462320052004, 80787, 7185202680], 'label': '77760.bo.1620.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.cv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.cv1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246055662
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.y1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.dd1', '810.bf1', '810.bn1'], 'contains': ['3240.bs2', '3240.bz1', '3240.ca1', '3240.do1', '3240.fv1', '4860.z1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [7185207845, 19679028004, 462320052004, 80787, 143304], 'label': '77760.bo.1620.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.cw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.cw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055663
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bs2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.cr1', '540.df1', '540.dg1', '810.bg1', '810.bl1', '810.br1'], 'contains': ['3240.bs1', '3240.bx1', '3240.cc1', '3240.dj1', '3240.dv1', '3240.fs1', '3240.hf1', '4860.ba1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [482947891, 362615, 87182202116, 80787, 375138086400], 'label': '77760.bo.1620.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.cx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.cx1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246055664
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bs2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.ca1', '540.dh1', '540.di1', '810.bh1', '810.bm1', '810.br1'], 'contains': ['3240.bs1', '3240.by1', '3240.db1', '3240.dy1', '3240.fw1', '4860.bb1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [83543730, 456053150130, 87261834387, 45813, 80787], 'label': '77760.bo.1620.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.cy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.cy1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246055665
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.cz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.cq1', '540.dj1', '540.dk1', '810.bi1', '810.bn1', '810.br1'], 'contains': ['3240.bs1', '3240.bs2', '3240.cc1', '3240.da1', '3240.da2', '3240.eb1', '3240.hg1', '4860.bc1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [317399, 448908278999, 19679028004, 462320052004, 80787], 'label': '77760.bo.1620.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '1620.cz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.cz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055666
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.cq1', '540.dl1', '540.dn1', '810.l1', '810.bo1', '810.bs1'], 'contains': ['3240.cd1', '3240.ee1', '3240.hh1', '4860.bc1', '6480.z1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [178680, 355462911480, 87661100280, 462320006400, 375138086400], 'label': '77760.bo.1620.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '1620.da1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.da1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055667
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.cq1', '540.dm1', '540.do1', '810.bp1'], 'contains': ['3240.ce1', '3240.ef1', '3240.hi1', '4860.bc1', '6480.ba1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841004800, 19678982400, 462320006400, 262496586694, 693], 'label': '77760.bo.1620.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bl1', 'old_label': '1620.db1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.db1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055668
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.f1', '540.cr1', '540.dp1', '540.dq1', '810.m1', '810.bq1', '810.bs1'], 'contains': ['3240.cd1', '3240.ei1', '3240.hl1', '4860.ba1', '6480.bb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [443120025600, 224184, 442641024000, 442162022400, 180667289784], 'label': '77760.bo.1620.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '1620.dc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.dc1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055669
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.dr1', '810.bg1', '810.bk1', '810.bl1'], 'contains': ['3240.bv1', '3240.bw1', '3240.bx1', '3240.ey1', '3240.ez1', '4860.bd1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [443120071204, 178680, 180667203842, 442641109705, 80787], 'label': '77760.bo.1620.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.dd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.dd1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055670
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.y1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.ds1', '810.bf1', '810.bl1'], 'contains': ['3240.bv2', '3240.bx1', '3240.bz1', '3240.fd1', '3240.fg1', '4860.be1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [178680, 19679028004, 462320046842, 80787, 7185202680], 'label': '77760.bo.1620.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.de1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.de1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055671
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.e1', '36.j1'], 'contains': ['144.a1', '144.f1', '144.g1', '216.c1', '216.g1', '360.bg1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [183845, 267842050314, 143975, 269202533759, 80880, 80787, 181146153355], 'label': '77760.bo.72.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '72.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1', 'subgroup_fusion': None, 'weyl_group': '2160.cr'}
  • id: 246055672
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.y1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.dt1', '810.bf1', '810.bm1', '810.bt1'], 'contains': ['3240.bv2', '3240.by1', '3240.ca1', '3240.fe1', '3240.ff1', '4860.bf1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [7185207845, 19679028004, 80787, 462320046985, 143304], 'label': '77760.bo.1620.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.df1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.df1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055673
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.cb1', '540.du1', '810.bh1', '810.bk1', '810.bt1'], 'contains': ['3240.bv1', '3240.by1', '3240.fo1', '3240.fp1', '4860.bg1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [83548555, 456053154955, 87261834387, 80787, 693], 'label': '77760.bo.1620.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.dg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.dg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055674
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.dv1', '810.bj1', '810.bk1', '810.bm1'], 'contains': ['3240.bw1', '3240.by1', '3240.go1', '3240.gp1', '4860.bh1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [87182277597, 282215, 374659447555, 355938110909, 80787], 'label': '77760.bo.1620.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.dh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.dh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055675
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.cu1', '540.dw1', '810.l1', '810.bq1', '810.bu1'], 'contains': ['3240.cd1', '3240.gw1', '4860.bj1', '6480.be1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [461841004800, 262496506293, 19678982400, 462320046985, 693], 'label': '77760.bo.1620.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '1620.di1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.di1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055676
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.cv1', '540.dx1', '810.bg1', '810.bn1', '810.bt1'], 'contains': ['3240.bv1', '3240.ca1', '3240.cc1', '3240.fb1', '3240.gy1', '4860.bi1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [443120071204, 180667289547, 178680, 442641109705, 80787], 'label': '77760.bo.1620.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.dj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.dj1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055677
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.g1', '540.cv1', '540.dy1', '810.m1', '810.bo1', '810.bu1'], 'contains': ['3240.cd1', '3240.ha1', '4860.bi1', '6480.bg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [443120025600, 178680, 442162022400, 180667244280, 442641109705], 'label': '77760.bo.1620.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '1620.dk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.dk1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055678
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.cv1', '540.dz1', '810.bp1'], 'contains': ['3240.ce1', '3240.hb1', '4860.bi1', '6480.bh1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [188331270027, 375138172205, 87182063304, 482773704, 143304], 'label': '77760.bo.1620.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bp1', 'old_label': '1620.dl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.dl1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055679
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.cu1', '540.ea1', '810.bi1', '810.bl1', '810.bt1'], 'contains': ['3240.bv1', '3240.bv2', '3240.cc1', '3240.fn1', '3240.hd1', '4860.bj1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [362615, 19679028004, 448908284158, 80787, 462320046985], 'label': '77760.bo.1620.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '1620.dm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.dm1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055680
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.cw1', '540.eb1', '810.bj1', '810.bl1', '810.bn1'], 'contains': ['3240.bw1', '3240.bz1', '3240.cc1', '3240.gl1', '3240.hr1', '4860.bk1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [355938191405, 362615, 87182202116, 80787, 374659447415], 'label': '77760.bo.1620.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.dn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.dn1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055681
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.cw1', '540.ec1', '810.n1', '810.bo1', '810.bq1'], 'contains': ['3240.cd1', '3240.ht1', '4860.bk1', '6480.bj1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [87182098680, 178680, 374659263480, 19203788280, 87657476645], 'label': '77760.bo.1620.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '1620.do1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.do1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055682
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.f1', '36.j1'], 'contains': ['144.a1', '144.g1', '144.h1', '216.d1', '216.h1', '360.bj1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [143975, 80787, 269202533759, 181146251274, 183845, 80880, 267842050314], 'label': '77760.bo.72.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '72.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1', 'subgroup_fusion': None, 'weyl_group': '2160.cr'}
  • id: 246055683
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.cw1', '540.ed1', '810.bp1'], 'contains': ['3240.ce1', '3240.hu1', '4860.bk1', '6480.bk1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [19203833547, 87182098680, 178680, 374659263480, 87657476645], 'label': '77760.bo.1620.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bp1', 'old_label': '1620.dp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.dp1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055684
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bs2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.cy1', '540.ee1', '540.ef1', '810.bj1', '810.br1', '810.bt1'], 'contains': ['3240.by1', '3240.cc1', '3240.gr1', '3240.hw1', '3240.ic1', '4860.bl1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [362615, 355938105600, 87182202116, 80787, 374659447415], 'label': '77760.bo.1620.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.dq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.dq1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246055685
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.n1', '540.cy1', '540.eg1', '540.eh1', '810.n1', '810.bs1', '810.bu1'], 'contains': ['3240.cd1', '3240.hz1', '3240.if1', '4860.bl1', '6480.bd1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [374659308984, 87182144184, 224184, 87657516984, 19203833784], 'label': '77760.bo.1620.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '1620.dr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.dr1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055686
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.cz1', '810.bd1', '810.bv1', '810.by1'], 'contains': ['3240.cf1', '3240.cf2', '3240.cg2', '3240.ci1', '3240.cj1', '3240.cs3', '3240.cs4', '3240.cu1', '3240.cx1', '3240.ej2', '3240.ev2', '4860.v1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [19679063280, 461841090505, 462320006400, 80880, 143304], 'label': '77760.bo.1620.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.ds1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ds1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055687
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ds2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.cz2', '810.bd1', '810.bw1', '810.bx1'], 'contains': ['3240.cf1', '3240.cf2', '3240.cg1', '3240.ci2', '3240.cj1', '3240.cs1', '3240.cs2', '3240.cu2', '3240.cx2', '3240.ej1', '3240.ev1', '4860.v2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [19679063280, 461841090505, 80880, 462320046985, 143304], 'label': '77760.bo.1620.ds2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.ds2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ds2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055688
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.cg1', '540.da1', '810.bc1', '810.bw1', '810.by1'], 'contains': ['3240.cg1', '3240.ci1', '3240.cm1', '3240.cv1', '3240.cz1', '3240.ek1', '3240.ew1', '4860.w1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [87261753748, 456053069398, 83467916, 148, 693], 'label': '77760.bo.1620.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.dt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.dt1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055689
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.db1', '810.bb1', '810.bx1', '810.by1'], 'contains': ['3240.cg1', '3240.cj1', '3240.cn1', '3240.dg1', '3240.di1', '3240.fx1', '3240.fy1', '4860.x1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [442641386187, 443120169575, 180667203842, 143975, 143304], 'label': '77760.bo.1620.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.du1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.du1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055690
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.dc1', '810.ba1', '810.bv1', '810.bz1'], 'contains': ['3240.cg2', '3240.ck1', '3240.cl1', '3240.dp1', '3240.dq1', '3240.gb1', '3240.gc1', '4860.y1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [19679063280, 462320006400, 80880, 7185202680, 143304], 'label': '77760.bo.1620.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1620.dv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.dv1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055691
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.dd1', '810.ba1', '810.by1'], 'contains': ['3240.cg2', '3240.cm1', '3240.cn1', '3240.dr1', '3240.ds1', '3240.gd1', '3240.ge1', '4860.z1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [7185207845, 462320368587, 19678982400, 143975, 143304], 'label': '77760.bo.1620.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.dw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.dw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055692
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.de1', '810.ca1'], 'contains': ['3240.ch2', '3240.co1', '3240.cp1', '3240.dt1', '3240.du1', '3240.gf1', '3240.gg1', '4860.y1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [462320368684, 178680, 19678982400, 7185202680, 179159], 'label': '77760.bo.1620.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '1620.dx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.dx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055693
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.a1', '24.b1', '36.g1', '36.h1', '36.i1'], 'contains': ['144.i1', '216.e1', '216.f1', '360.bm1', '432.c1', '720.bd1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [183845, 455574246212, 143975, 349232267045, 80787], 'label': '77760.bo.72.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '72.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1', 'subgroup_fusion': None, 'weyl_group': '12960.bv'}
  • id: 246055694
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.v2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.df1', '540.dp1', '810.bb1', '810.bw1', '810.bz1'], 'contains': ['3240.cg1', '3240.ck1', '3240.cq1', '3240.dk1', '3240.dw1', '3240.fz1', '3240.hj1', '4860.ba1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [224184, 443120250115, 180667289784, 224515, 442641305788], 'label': '77760.bo.1620.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1620.dy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.dy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055695
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.dg1', '540.dq1', '810.ca1'], 'contains': ['3240.ch1', '3240.co1', '3240.cr1', '3240.dl1', '3240.dx1', '3240.ga1', '3240.hk1', '4860.ba1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [375138265559, 482809080, 178680, 87182282615, 179159], 'label': '77760.bo.1620.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '1620.dz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.dz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055696
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.v2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.ch1', '540.dh1', '810.bc1', '810.bx1', '810.bz1'], 'contains': ['3240.cg1', '3240.cl1', '3240.de1', '3240.dz1', '3240.gh1', '4860.bb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [224184, 456053069398, 83462998, 87262035388, 224515], 'label': '77760.bo.1620.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1620.ea1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ea1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055697
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.ci1', '540.di1', '810.ca1'], 'contains': ['3240.ch1', '3240.cp1', '3240.df1', '3240.ea1', '3240.gi1', '4860.bb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [87262115884, 178680, 456053069398, 83462998, 179159], 'label': '77760.bo.1620.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '1620.eb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.eb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055698
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.bq1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.dj1', '540.dl1', '540.dm1', '810.bd1', '810.by1', '810.bz1'], 'contains': ['3240.cg1', '3240.cg2', '3240.cq1', '3240.dc1', '3240.dc2', '3240.ec1', '3240.ho1', '4860.bc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [462320288188, 224184, 19678982400, 224515, 448908243571], 'label': '77760.bo.1620.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '1620.ec1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ec1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055699
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.dk1', '540.dn1', '540.do1', '810.ca1'], 'contains': ['3240.ch1', '3240.ch2', '3240.cr1', '3240.dd1', '3240.dd2', '3240.ed1', '3240.hp1', '4860.bc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [462320287944, 19678982400, 143731, 448908243571, 143304], 'label': '77760.bo.1620.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '1620.ed1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ed1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055700
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.dr1', '810.bb1', '810.bv1', '810.bw1'], 'contains': ['3240.ci1', '3240.cj1', '3240.ck1', '3240.el1', '3240.em1', '3240.ex1', '3240.fa1', '4860.bd1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [143975, 375138270474, 482814245, 87182282615, 143304], 'label': '77760.bo.1620.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.ee1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ee1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055701
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.ds1', '810.ba1', '810.bw1'], 'contains': ['3240.ci2', '3240.ck1', '3240.cm1', '3240.eo1', '3240.er1', '3240.fh1', '3240.fk1', '4860.be1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [19679063280, 80880, 7185202680, 462320046985, 143304], 'label': '77760.bo.1620.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.ef1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ef1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055702
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.dt1', '810.ba1', '810.bx1', '810.cb1'], 'contains': ['3240.ci2', '3240.cl1', '3240.cn1', '3240.ep1', '3240.eq1', '3240.fi1', '3240.fj1', '4860.bf1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [7185207845, 462320283121, 19678982400, 143975, 143304], 'label': '77760.bo.1620.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.eg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.eg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055703
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.cm1', '540.du1', '810.bc1', '810.bv1', '810.cb1'], 'contains': ['3240.ci1', '3240.cl1', '3240.es1', '3240.fm1', '3240.fq1', '4860.bg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [83548555, 456053154955, 143975, 87262115787, 143304], 'label': '77760.bo.1620.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.eh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.eh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055704
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '36.j1'], 'contains': ['144.a1', '144.b1', '144.c1', '144.d1', '144.e1', '216.i1', '360.bt1'], 'core': '720.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18764743922, 1037980104, 143975, 85805, 80880, 80787, 143304], 'label': '77760.bo.72.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '72.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1', 'subgroup_fusion': None, 'weyl_group': '2160.cr'}
  • id: 246055705
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.dv1', '810.be1', '810.bv1', '810.bx1'], 'contains': ['3240.cj1', '3240.cl1', '3240.gk1', '3240.gn1', '3240.gq1', '4860.bh1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [87182277597, 179012, 178680, 355938191305, 374659402052], 'label': '77760.bo.1620.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.ei1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ei1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055706
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.dx1', '540.dy1', '540.dz1', '810.bb1', '810.by1', '810.cb1'], 'contains': ['3240.ci1', '3240.cn1', '3240.cq1', '3240.en1', '3240.fc1', '3240.gu1', '3240.gz1', '4860.bi1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [443120025600, 180667289784, 442641109705, 80880, 143304], 'label': '77760.bo.1620.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.ej1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ej1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055707
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.dw1', '540.ea1', '810.bd1', '810.bw1', '810.cb1'], 'contains': ['3240.ci1', '3240.ci2', '3240.cq1', '3240.fl1', '3240.fl2', '3240.gv1', '3240.he1', '4860.bj1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [19678982400, 143975, 448908284158, 462320328386, 143304], 'label': '77760.bo.1620.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '1620.ek1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ek1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055708
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.eb1', '540.ec1', '540.ed1', '810.be1', '810.bw1', '810.by1'], 'contains': ['3240.cj1', '3240.cm1', '3240.cq1', '3240.gj1', '3240.gm1', '3240.hq1', '3240.hs1', '4860.bk1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [362615, 45363, 355938110909, 87182282615, 374659402052], 'label': '77760.bo.1620.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.el1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.el1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055709
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.v2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.ee1', '540.eg1', '810.be1', '810.bz1', '810.cb1'], 'contains': ['3240.cl1', '3240.cq1', '3240.gs1', '3240.hx1', '3240.id1', '4860.bl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [355938105600, 143975, 87182282615, 374659447415, 143304], 'label': '77760.bo.1620.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1620.em1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.em1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055710
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.ef1', '540.eh1', '810.ca1'], 'contains': ['3240.cp1', '3240.cr1', '3240.gt1', '3240.hy1', '3240.ie1', '4860.bl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [355938105600, 178680, 87182282615, 374659447415, 179159], 'label': '77760.bo.1620.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '1620.en1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.en1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055711
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.ei1', '810.d1', '810.o1', '810.by1'], 'contains': ['3240.cu1', '3240.dc1', '3240.ds1', '3240.ek1', '3240.en1', '3240.fx1', '3240.gj1', '4860.bm1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841009961, 462320288188, 19678982400, 224515, 448908243571], 'label': '77760.bo.1620.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.eo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.eo1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055712
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.ej1', '810.c1', '810.q1', '810.by1'], 'contains': ['3240.cv1', '3240.dc2', '3240.di1', '3240.ej2', '3240.en1', '3240.gd1', '3240.gm1', '4860.bm2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841090505, 448908042244, 45363, 19679027763, 462320369015], 'label': '77760.bo.1620.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.ep1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ep1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055713
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.ek1', '810.d1', '810.q1', '810.bx1'], 'contains': ['3240.cu2', '3240.de1', '3240.di1', '3240.ej1', '3240.eq1', '3240.fx1', '3240.gn1', '4860.bn1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841009961, 462320283029, 19678982400, 224515, 448908243571], 'label': '77760.bo.1620.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.eq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.eq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055714
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.d2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.el1', '810.h1', '810.o1', '810.bv1'], 'contains': ['3240.cu1', '3240.dp1', '3240.el1', '3240.es1', '3240.gk1', '4860.bp1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [462320288188, 448908283441, 19678982400, 224515, 461841090746], 'label': '77760.bo.1620.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.er1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.er1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246055715
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.h1', '24.c1', '36.i1', '36.l1', '36.n1'], 'contains': ['144.i1', '216.j1', '216.n1', '360.ci1', '432.f1', '720.by1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [286483098115, 143975, 80787, 25470771715, 143304], 'label': '77760.bo.72.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1', 'subgroup_fusion': None, 'weyl_group': '1440.5849'}
  • id: 246055716
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.ei1', '540.en1', '810.p1', '810.v1', '810.bn1'], 'contains': ['3240.cw1', '3240.da1', '3240.do1', '3240.eu1', '3240.fb1', '3240.fr1', '3240.gl1', '4860.bm1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [448908278999, 461841009961, 19679028004, 462320052004, 80787], 'label': '77760.bo.1620.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.es1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.es1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055717
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.es2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.ej1', '540.em1', '810.r1', '810.t1', '810.bn1'], 'contains': ['3240.cy1', '3240.da2', '3240.dh1', '3240.et2', '3240.fb1', '3240.fv1', '3240.gl1', '4860.bm2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [448908007204, 461841090505, 462320323652, 19679028004, 80787], 'label': '77760.bo.1620.es2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.es2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.es2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055718
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.ek1', '540.eo1', '810.r1', '810.v1', '810.bm1'], 'contains': ['3240.cw2', '3240.db1', '3240.dh1', '3240.et1', '3240.ff1', '3240.fr1', '3240.gp1', '4860.bn1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [448908278999, 461841327358, 19679028004, 462320328958, 80787], 'label': '77760.bo.1620.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.et1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.et1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055719
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.em1', '810.b1', '810.s1', '810.by1'], 'contains': ['3240.cz1', '3240.dc2', '3240.dg1', '3240.ev2', '3240.fc1', '3240.ge1', '3240.gj1', '4860.bm2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841090505, 179012, 462320323652, 19678982400, 448908278520], 'label': '77760.bo.1620.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.eu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.eu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055720
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.en1', '810.a1', '810.u1', '810.by1'], 'contains': ['3240.cx1', '3240.dc1', '3240.dr1', '3240.ew1', '3240.fc1', '3240.fy1', '3240.gm1', '4860.bm1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [19679063280, 461841183480, 448908001949, 462320006400, 80880], 'label': '77760.bo.1620.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.ev1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ev1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055721
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.eo1', '810.b1', '810.u1', '810.bx1'], 'contains': ['3240.cx2', '3240.de1', '3240.dg1', '3240.ev1', '3240.fj1', '3240.fy1', '3240.gn1', '4860.bn1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841090505, 45363, 448908243571, 19679027763, 462320011466], 'label': '77760.bo.1620.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.ew1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ew1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055722
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.ep1', '810.d1', '810.s1', '810.bw1'], 'contains': ['3240.cu2', '3240.cz1', '3240.dk1', '3240.er1', '3240.ex1', '3240.fl1', '3240.gj1', '4860.bo1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [19679063280, 462320190245, 448908001949, 461841143189, 80880], 'label': '77760.bo.1620.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.ex1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ex1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055723
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.eq1', '810.c1', '810.u1', '810.bw1'], 'contains': ['3240.cv1', '3240.cx2', '3240.dk1', '3240.em1', '3240.fk1', '3240.fl2', '3240.gm1', '4860.bo1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [448908283441, 461841143042, 19678982400, 224515, 462320328958], 'label': '77760.bo.1620.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.ey1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ey1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055724
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.er1', '810.d1', '810.u1', '810.bv1'], 'contains': ['3240.cu1', '3240.cx1', '3240.dq1', '3240.em1', '3240.ex1', '3240.fm1', '3240.gn1', '4860.bq1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841090505, 45363, 462320006400, 448908283914, 19679027763], 'label': '77760.bo.1620.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.ez1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ez1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055725
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.ep1', '540.eq1', '810.t1', '810.v1', '810.bl1'], 'contains': ['3240.cw2', '3240.cy1', '3240.dj1', '3240.ez1', '3240.fg1', '3240.fn1', '3240.gl1', '4860.bo1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841223825, 462320225425, 19679028004, 448908001949, 80787], 'label': '77760.bo.1620.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.fa1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.fa1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055726
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['12.e1', '12.f1', '12.g1', '12.j1', '12.k1', '18.i1', '30.g1', '36.j1', '60.o1'], 'core': '720.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [174879492452, 143975, 85805, 80880, 80787, 462320328386, 143304], 'label': '77760.bo.6.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '6.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1', 'subgroup_fusion': None, 'weyl_group': '12960.bv'}
  • id: 246055727
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.i1', '24.c1', '36.m1'], 'contains': ['144.j1', '216.j1', '216.o1', '360.cj1', '432.g1', '720.bz1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [286483052759, 25470726359, 80787, 143304, 179159], 'label': '77760.bo.72.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.m1', 'old_label': '72.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 246055728
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.cg2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.el1', '540.es1', '810.p1', '810.w1', '810.bk1'], 'contains': ['3240.cw1', '3240.dm1', '3240.ey1', '3240.fo1', '3240.go1', '4860.bp1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [461841327358, 19679028004, 462320052004, 448908284158, 80787], 'label': '77760.bo.1620.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1620.fb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.fb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055729
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.er1', '810.v1', '810.bk1'], 'contains': ['3240.cw1', '3240.dn1', '3240.ez1', '3240.fp1', '3240.gp1', '4860.bq1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [461841090505, 19679028004, 462320052004, 448908284158, 80787], 'label': '77760.bo.1620.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.fc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.fc1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055730
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.es1', '810.a1', '810.x1', '810.bv1'], 'contains': ['3240.cx1', '3240.dp1', '3240.fa1', '3240.fq1', '3240.gq1', '4860.bp1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [19679063280, 448908001949, 461841010109, 462320006400, 80880], 'label': '77760.bo.1620.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.fd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.fd1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055731
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bs2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.et1', '540.eu1', '810.p1', '810.br1'], 'contains': ['3240.da1', '3240.dm1', '3240.fs1', '3240.fw1', '3240.gr1', '4860.br1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [448908278999, 461841286771, 19679028004, 462320052004, 80787], 'label': '77760.bo.1620.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.fe1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.fe1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246055732
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.v2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.et1', '810.a1', '810.o1', '810.bz1'], 'contains': ['3240.dc1', '3240.dp1', '3240.fz1', '3240.gh1', '3240.gs1', '4860.br1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [462320288188, 19678982400, 224515, 448908243571, 461841228984], 'label': '77760.bo.1620.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1620.ff1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ff1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055733
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.eu1', '810.ca1'], 'contains': ['3240.dd1', '3240.dt1', '3240.ga1', '3240.gi1', '3240.gt1', '4860.br1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [462320287944, 19678982400, 143731, 461841148104, 448908243571], 'label': '77760.bo.1620.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '1620.fg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.fg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055734
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.d2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.ev1', '540.fs1', '810.h1', '810.q1', '810.bw1'], 'contains': ['3240.cu2', '3240.cv1', '3240.dw1', '3240.el1', '3240.eo1', '3240.gv1', '3240.hq1', '4860.bs1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [45363, 462320363997, 461841281758, 448908283914, 19679027763], 'label': '77760.bo.1620.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.fh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.fh1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246055735
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.cg2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.ev1', '540.ew1', '540.ft1', '810.r1', '810.w1', '810.bl1'], 'contains': ['3240.cw2', '3240.cy1', '3240.dv1', '3240.ey1', '3240.fd1', '3240.hd1', '3240.hr1', '4860.bs1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841009961, 19679028004, 448908001949, 80787, 462320046749], 'label': '77760.bo.1620.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1620.fi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.fi1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055736
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.ew1', '540.fu1', '810.b1', '810.x1', '810.bw1'], 'contains': ['3240.cx2', '3240.cz1', '3240.dw1', '3240.fa1', '3240.fh1', '3240.he1', '3240.hs1', '4860.bs1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841223825, 19678982400, 143975, 448908284158, 462320328958], 'label': '77760.bo.1620.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.fj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.fj1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055737
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bs2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.ex1', '540.ey1', '540.fv1', '810.r1', '810.br1'], 'contains': ['3240.da2', '3240.db1', '3240.dv1', '3240.fs1', '3240.ft1', '3240.hg1', '3240.hw1', '4860.bt1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [448908278999, 462320323799, 461841286771, 19679028004, 80787], 'label': '77760.bo.1620.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.fk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.fk1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246055738
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '36.j1'], 'contains': ['144.d1', '144.f1', '144.h1', '216.k1', '216.m1', '360.cs1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [181146067893, 143975, 269202609094, 267842045399, 80880, 80787, 143304], 'label': '77760.bo.72.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '72.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 246055739
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.v2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.ex1', '540.fw1', '810.b1', '810.q1', '810.bz1'], 'contains': ['3240.dc2', '3240.de1', '3240.dw1', '3240.fz1', '3240.gb1', '3240.ho1', '3240.hx1', '4860.bt1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841004800, 19678982400, 143975, 448908323787, 462320369015], 'label': '77760.bo.1620.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1620.fl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.fl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055740
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.ey1', '540.fx1', '810.ca1'], 'contains': ['3240.dd2', '3240.df1', '3240.dx1', '3240.ga1', '3240.gf1', '3240.hp1', '3240.hy1', '4860.bt1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [462320288371, 19678982400, 143731, 461841148104, 448908243571], 'label': '77760.bo.1620.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '1620.fm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.fm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055741
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.d2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.ez1', '810.h1', '810.s1', '810.bx1'], 'contains': ['3240.cu2', '3240.dg1', '3240.dz1', '3240.ep1', '3240.gk1', '4860.bu1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [19679063280, 462320225425, 448908007104, 461841188401, 80880], 'label': '77760.bo.1620.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.fn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.fn1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246055742
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.cg2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.ez1', '540.fa1', '810.t1', '810.w1', '810.bm1'], 'contains': ['3240.cw2', '3240.dh1', '3240.dy1', '3240.fe1', '3240.go1', '4860.bu1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [461841223825, 448908007204, 462320225425, 19679028004, 80787], 'label': '77760.bo.1620.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1620.fo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.fo1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055743
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.fa1', '810.c1', '810.x1', '810.bx1'], 'contains': ['3240.cx2', '3240.di1', '3240.dz1', '3240.fi1', '3240.gq1', '4860.bu1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [461841223825, 19678982400, 143975, 448908323787, 462320328958], 'label': '77760.bo.1620.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.fp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.fp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055744
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bs2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.fb1', '540.fc1', '810.t1', '810.br1'], 'contains': ['3240.da2', '3240.dj1', '3240.dy1', '3240.fu1', '3240.gr1', '4860.bv1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [448908007204, 19679028004, 461841148348, 80787, 462320230347], 'label': '77760.bo.1620.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.fq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.fq1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246055745
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.v2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.fb1', '810.c1', '810.s1', '810.bz1'], 'contains': ['3240.dc2', '3240.dk1', '3240.dz1', '3240.gc1', '3240.gs1', '4860.bv1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [19679063280, 461841183480, 448908007104, 462320149704, 80880], 'label': '77760.bo.1620.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1620.fr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.fr1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055746
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.fc1', '810.ca1'], 'contains': ['3240.dd2', '3240.dl1', '3240.ea1', '3240.gg1', '3240.gt1', '4860.bv1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [461841183480, 19678982400, 448908323884, 462320369015, 179159], 'label': '77760.bo.1620.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '1620.fs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.fs1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055747
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.d2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.fd1', '540.fe1', '540.ff1', '810.h1', '810.u1', '810.by1'], 'contains': ['3240.cu1', '3240.cv1', '3240.dg1', '3240.dr1', '3240.ec1', '3240.gu1', '3240.hq1', '4860.bw1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841050163, 45363, 462320006400, 448908283914, 19679027763], 'label': '77760.bo.1620.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.ft1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ft1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246055748
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.cg2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.fd1', '540.fg1', '540.fh1', '540.fi1', '810.v1', '810.w1', '810.bn1'], 'contains': ['3240.cw1', '3240.cy1', '3240.dh1', '3240.do1', '3240.eb1', '3240.gy1', '3240.hr1', '4860.bw1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841223825, 448908007204, 19679028004, 462320052004, 80787], 'label': '77760.bo.1620.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1620.fu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.fu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055749
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '36.j1'], 'contains': ['144.d1', '144.g1', '216.l1', '360.cv1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [143975, 80787, 267842045399, 269202609094, 143304, 181146153355, 80880], 'label': '77760.bo.72.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '72.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1', 'subgroup_fusion': None, 'weyl_group': '2160.cr'}
  • id: 246055750
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.fg1', '540.fj1', '540.fk1', '810.d1', '810.x1', '810.by1'], 'contains': ['3240.cx1', '3240.cz1', '3240.di1', '3240.ds1', '3240.ec1', '3240.gz1', '3240.hs1', '4860.bw1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [19679063280, 461841090505, 448908007104, 462320006400, 80880], 'label': '77760.bo.1620.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.fv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.fv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055751
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.fe1', '540.fh1', '540.fj1', '810.e1', '810.i1', '810.bo1'], 'contains': ['3240.ee1', '3240.ha1', '3240.ht1', '4860.bw1', '6480.bu1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841004800, 19678982400, 448908284158, 462320006400, 262496505600], 'label': '77760.bo.1620.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '1620.fw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.fw1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055752
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.ff1', '540.fh1', '540.fk1', '810.bp1'], 'contains': ['3240.ef1', '3240.hb1', '3240.hu1', '4860.bw1', '6480.bv1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [355462813587, 482849425, 87660921600, 462320006400, 375138086400], 'label': '77760.bo.1620.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bu1', 'old_label': '1620.fx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.fx1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055753
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.fi1', '540.fj1', '540.fk1', '810.f1'], 'contains': ['3240.eg1', '3240.hc1', '3240.hv1', '4860.bw1', '6480.bw1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [461841004800, 19678982400, 448908284158, 462320006400, 262496684612], 'label': '77760.bo.1620.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.f1', 'old_label': '1620.fy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.fy1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055754
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bs2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.fl1', '540.fm1', '540.fn1', '540.fo1', '540.fp1', '810.v1', '810.br1'], 'contains': ['3240.da1', '3240.db1', '3240.dj1', '3240.dn1', '3240.eb1', '3240.hf1', '3240.hw1', '4860.bx1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [448908278999, 19679028004, 462320052004, 461841050404, 80787], 'label': '77760.bo.1620.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.fz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.fz1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246055755
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.v2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.fl1', '540.fq1', '810.d1', '810.u1', '810.bz1'], 'contains': ['3240.dc1', '3240.de1', '3240.dk1', '3240.dq1', '3240.ec1', '3240.hj1', '3240.hx1', '4860.bx1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [19679063280, 461841183480, 448908007104, 462320006400, 80880], 'label': '77760.bo.1620.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1620.ga1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ga1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055756
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.fm1', '540.fr1', '810.ca1'], 'contains': ['3240.dd1', '3240.df1', '3240.dl1', '3240.du1', '3240.ed1', '3240.hk1', '3240.hy1', '4860.bx1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841004800, 462320287944, 19678982400, 143731, 448908243571], 'label': '77760.bo.1620.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '1620.gb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.gb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055757
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.fn1', '540.fq1', '540.fr1', '810.e1', '810.bs1'], 'contains': ['3240.ee1', '3240.hl1', '3240.hz1', '4860.bx1', '6480.ca1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [461841004800, 19678982400, 448908243571, 462320006400, 262496505600], 'label': '77760.bo.1620.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '1620.gc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.gc1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055758
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.fo1', '540.fq1', '810.f1'], 'contains': ['3240.eg1', '3240.hm1', '3240.ia1', '4860.bx1', '6480.cb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [461841004800, 262496730115, 19678982400, 448908243571, 462320006400], 'label': '77760.bo.1620.gd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.l1', 'old_label': '1620.gd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.gd1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055759
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.fp1', '540.fr1'], 'contains': ['3240.eh1', '3240.hn1', '3240.ib1', '4860.bx1', '6480.cc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [482854584, 87660921600, 462320006400, 355462957412, 375138086400], 'label': '77760.bo.1620.ge1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.fp1', 'old_label': '1620.ge1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ge1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055760
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.b1', '24.d1', '36.c1', '36.g1', '36.l1'], 'contains': ['144.i1', '216.p1', '216.q1', '360.do1', '432.i1', '720.dm1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [462320323320, 143975, 174879491787, 80787], 'label': '77760.bo.72.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '72.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.k1', 'subgroup_fusion': None, 'weyl_group': '1440.5849'}
  • id: 246055761
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.fs1', '540.ft1', '540.fu1', '810.g1', '810.i1', '810.bq1'], 'contains': ['3240.ei1', '3240.gw1', '3240.ht1', '4860.bs1', '6480.cg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841004800, 19678982400, 448907961600, 462320328958, 262496505600], 'label': '77760.bo.1620.gf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '1620.gf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.gf1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055762
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.fv1', '540.fw1', '540.fx1', '810.g1', '810.bs1'], 'contains': ['3240.ei1', '3240.hh1', '3240.hz1', '4860.bt1', '6480.ch1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [461841004800, 19678982400, 448907961600, 262496505600, 462320369015], 'label': '77760.bo.1620.gg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '1620.gg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.gg1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055763
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.cp2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.fy1', '540.fz1', '540.ga1', '810.w1', '810.br1'], 'contains': ['3240.dm1', '3240.dv1', '3240.dy1', '3240.eb1', '3240.ic1', '4860.by1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [448908007204, 19679028004, 462320052004, 461841050404, 80787], 'label': '77760.bo.1620.gh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '1620.gh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.gh1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246055764
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.r2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.fy1', '540.gb1', '810.h1', '810.x1', '810.bz1'], 'contains': ['3240.dp1', '3240.dw1', '3240.dz1', '3240.ec1', '3240.id1', '4860.by1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [461841004800, 462320368587, 19678982400, 143975, 448908323787], 'label': '77760.bo.1620.gi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1620.gi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.gi1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246055765
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.dk2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.fz1', '540.gc1', '810.ca1'], 'contains': ['3240.dt1', '3240.dx1', '3240.ea1', '3240.ed1', '3240.ie1', '4860.by1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [461841004800, 462320368684, 19678982400, 448908323884, 179159], 'label': '77760.bo.1620.gj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '1620.gj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.gj1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246055766
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.bs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.a1', '540.ga1', '540.gb1', '540.gc1', '810.i1', '810.bs1'], 'contains': ['3240.ee1', '3240.ei1', '3240.if1', '4860.by1', '6480.ci1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [355462732800, 482630400, 87660921600, 462320006400, 375138086400], 'label': '77760.bo.1620.gk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '1620.gk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.gk1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055767
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.gd1', '810.a1', '810.y1', '810.bx1'], 'contains': ['3240.ej1', '3240.ep1', '3240.fy1', '3240.gh1', '3240.gq1', '4860.bz1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [461841223825, 462320283029, 19678982400, 224515, 448908243571], 'label': '77760.bo.1620.gl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.gl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.gl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055768
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.ge1', '810.c1', '810.y1', '810.bv1'], 'contains': ['3240.ej2', '3240.em1', '3240.es1', '3240.gc1', '3240.gq1', '4860.cc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [461841090505, 45363, 448908283914, 19679027763, 462320369015], 'label': '77760.bo.1620.gm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.gm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.gm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055769
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.gd1', '540.gf1', '810.p1', '810.z1', '810.bm1'], 'contains': ['3240.et1', '3240.fe1', '3240.fr1', '3240.fw1', '3240.go1', '4860.bz1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [448908278999, 461841327358, 19679028004, 80787, 462320046749], 'label': '77760.bo.1620.gn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.gn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.gn1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055770
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.gf1', '810.j1', '810.o1', '810.bx1'], 'contains': ['3240.ev1', '3240.fi1', '3240.fx1', '3240.gh1', '3240.gk1', '4860.bz1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [45363, 448908243571, 461841281758, 19679027763, 462320011466], 'label': '77760.bo.1620.go1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.go1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.go1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055771
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.l1', '24.d1', '36.m1'], 'contains': ['144.j1', '216.p1', '216.r1', '360.dp1', '432.m1', '720.dn1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [174879491884, 462320323467, 80787, 179159], 'label': '77760.bo.72.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '72.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.l1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 246055772
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gg1', '810.b1', '810.o1', '810.bw1'], 'contains': ['3240.ek1', '3240.el1', '3240.ev1', '3240.fh1', '3240.fl2', '3240.fz1', '3240.gj1', '4860.ca1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [19678982400, 224515, 448908243571, 462320328958, 461841228984], 'label': '77760.bo.1620.gp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.gp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.gp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055773
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gh1', '810.a1', '810.q1', '810.bw1'], 'contains': ['3240.ej1', '3240.eo1', '3240.ew1', '3240.fa1', '3240.fl1', '3240.fz1', '3240.gm1', '4860.ca1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841322052, 45363, 448908243571, 462320328958, 19679027763], 'label': '77760.bo.1620.gq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.gq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.gq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055774
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gi1', '810.b1', '810.q1', '810.bv1'], 'contains': ['3240.ej2', '3240.el1', '3240.ev2', '3240.fa1', '3240.fm1', '3240.gb1', '3240.gn1', '4860.cb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841090505, 45363, 448908001949, 19679027763, 462320369015], 'label': '77760.bo.1620.gr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.gr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.gr1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055775
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.gs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.gj1', '810.c1', '810.o1', '810.cb1'], 'contains': ['3240.en1', '3240.es1', '3240.fi1', '3240.fl2', '3240.gs1', '4860.cd1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [448908283441, 19678982400, 224515, 462320328958, 461841228984], 'label': '77760.bo.1620.gs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.gs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.gs1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055776
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.gt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gg1', '540.gh1', '810.p1', '810.r1', '810.bl1'], 'contains': ['3240.et1', '3240.eu1', '3240.ey1', '3240.fd1', '3240.fn1', '3240.fs1', '3240.gl1', '4860.ca1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [448908278999, 461841286771, 19679028004, 462320328958, 80787], 'label': '77760.bo.1620.gt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.gt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.gt1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055777
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.gu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.gi1', '810.r1', '810.bk1'], 'contains': ['3240.et2', '3240.ey1', '3240.fp1', '3240.ft1', '3240.gp1', '4860.cb1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [461841009961, 462320323799, 19679028004, 448908001949, 80787], 'label': '77760.bo.1620.gu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.gu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.gu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055778
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.gv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.ge1', '540.gk1', '810.t1', '810.z1', '810.bk1'], 'contains': ['3240.et2', '3240.ez1', '3240.fo1', '3240.fu1', '3240.go1', '4860.cc1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [461841090505, 462320323652, 19679028004, 448908284158, 80787], 'label': '77760.bo.1620.gv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.gv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.gv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055779
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.gw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.gk1', '810.j1', '810.s1', '810.bv1'], 'contains': ['3240.ev2', '3240.ex1', '3240.fq1', '3240.gc1', '3240.gk1', '4860.cc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [179012, 462320323652, 19678982400, 448908284158, 461841010109], 'label': '77760.bo.1620.gw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.gw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.gw1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055780
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.gx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.gl1', '810.a1', '810.s1', '810.cb1'], 'contains': ['3240.ep1', '3240.fc1', '3240.fl1', '3240.fq1', '3240.gs1', '4860.cd1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [19679063280, 462320190245, 461841183480, 448908001949, 80880], 'label': '77760.bo.1620.gx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.gx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.gx1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055781
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.gy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.gj1', '540.gl1', '810.p1', '810.t1', '810.bt1'], 'contains': ['3240.fb1', '3240.fe1', '3240.fn1', '3240.fo1', '3240.gr1', '4860.cd1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [462320225425, 19679028004, 448908001949, 461841183388, 80787], 'label': '77760.bo.1620.gy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.gy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.gy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055782
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.m1', '24.e1', '36.c1', '36.h1', '36.n1'], 'contains': ['144.i1', '216.s1', '216.t1', '360.ew1', '432.j1', '720.eb1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [143975, 174879406321, 80787, 462320328386], 'label': '77760.bo.72.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.m1', 'subgroup_fusion': None, 'weyl_group': '1440.5849'}
  • id: 246055783
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.gz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gn1', '540.go1', '540.gp1', '810.b1', '810.y1', '810.by1'], 'contains': ['3240.ej2', '3240.ek1', '3240.fy1', '3240.ge1', '3240.gu1', '3240.ho1', '3240.hs1', '4860.ce1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841050163, 45363, 448908283914, 19679027763, 462320369015], 'label': '77760.bo.1620.gz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.gz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.gz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055784
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ha1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gm1', '540.gq1', '810.d1', '810.y1', '810.bw1'], 'contains': ['3240.ej1', '3240.ek1', '3240.em1', '3240.er1', '3240.gv1', '3240.hj1', '3240.hs1', '4860.cf1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841050163, 45363, 448908243571, 462320328958, 19679027763], 'label': '77760.bo.1620.ha1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.ha1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ha1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055785
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.hb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gm1', '540.gr1', '540.gt1', '810.e1', '810.k1', '810.bq1'], 'contains': ['3240.gw1', '3240.hl1', '3240.ht1', '4860.cf1', '6480.dx1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [355462732800, 482635561, 375138363450, 87661198650, 462320283450], 'label': '77760.bo.1620.hb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '1620.hb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.hb1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055786
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.hc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gm1', '540.gs1', '810.f1'], 'contains': ['3240.gx1', '3240.hm1', '3240.hv1', '4860.cf1', '6480.dy1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [461841004800, 262496730115, 19678982400, 448908243571, 462320046749], 'label': '77760.bo.1620.hc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.f1', 'old_label': '1620.hc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.hc1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055787
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.hd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gn1', '540.gu1', '540.gv1', '810.r1', '810.z1', '810.bn1'], 'contains': ['3240.et2', '3240.eu1', '3240.fr1', '3240.fv1', '3240.gy1', '3240.hg1', '3240.hr1', '4860.ce1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [462320323891, 19679028004, 448908284158, 461841050404, 80787], 'label': '77760.bo.1620.hd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.hd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.hd1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055829
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.e1', '720.s1', '720.v1', '1080.d1', '1080.m1'], 'contains': ['4320.d1', '4320.dg1', '4320.dr1', '6480.l1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [5161, 482849425, 280259486761, 193999276800], 'label': '77760.bo.2160.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.e1', 'old_label': '2160.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.m1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246055788
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.he1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.go1', '540.gu1', '540.gw1', '810.g1', '810.k1', '810.bo1'], 'contains': ['3240.ha1', '3240.hh1', '3240.ht1', '4860.ce1', '6480.ea1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [355462732800, 87661064904, 482849425, 462320149704, 375138229704], 'label': '77760.bo.1620.he1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '1620.he1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.he1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055789
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.hf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gp1', '540.gu1', '540.gx1', '810.bp1'], 'contains': ['3240.hb1', '3240.hi1', '3240.hu1', '4860.ce1', '6480.eb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [461841004800, 462320288371, 19678982400, 448908001949, 262496586387], 'label': '77760.bo.1620.hf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bp1', 'old_label': '1620.hf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.hf1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055790
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.hg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gv1', '540.gw1', '540.gx1', '810.j1', '810.q1', '810.by1'], 'contains': ['3240.ev2', '3240.ew1', '3240.fx1', '3240.gd1', '3240.gz1', '3240.ho1', '3240.hq1', '4860.ce1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841004800, 19678982400, 143975, 448908284158, 462320369015], 'label': '77760.bo.1620.hg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.hg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.hg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055791
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.hh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gz1', '540.ha1', '810.d1', '810.q1', '810.cb1'], 'contains': ['3240.en1', '3240.eq1', '3240.fl1', '3240.fm1', '3240.gv1', '3240.gz1', '3240.hx1', '4860.cg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841322052, 45363, 462320363997, 448908283914, 19679027763], 'label': '77760.bo.1620.hh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.hh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.hh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055792
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.hi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gy1', '540.gz1', '540.hb1', '810.e1', '810.g1', '810.bu1'], 'contains': ['3240.gw1', '3240.ha1', '3240.hz1', '4860.cg1', '6480.ee1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841004800, 19678982400, 448908001949, 462320363997, 262496505600], 'label': '77760.bo.1620.hi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '1620.hi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.hi1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055793
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.c1', '24.e1', '36.d1', '36.g1', '36.n1'], 'contains': ['144.i1', '216.t1', '216.u1', '360.fc1', '432.k1', '720.ec1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [174879215546, 80880, 80787, 462320046985], 'label': '77760.bo.72.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '72.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.n1', 'subgroup_fusion': None, 'weyl_group': '12960.bv'}
  • id: 246055794
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.hj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gz1', '540.hc1', '810.f1'], 'contains': ['3240.gx1', '3240.hc1', '3240.ia1', '4860.cg1', '6480.ef1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [461841004800, 19678982400, 262496550963, 448908001949, 462320363997], 'label': '77760.bo.1620.hj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.f1', 'old_label': '1620.hj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.hj1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055795
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.hk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gq1', '540.gr1', '540.gs1', '540.hd1', '810.v1', '810.z1', '810.bl1'], 'contains': ['3240.et1', '3240.eu1', '3240.ez1', '3240.fg1', '3240.hd1', '3240.hf1', '3240.hr1', '4860.cf1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [448908278999, 19679028004, 461841050404, 462320328958, 80787], 'label': '77760.bo.1620.hk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.hk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.hk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055796
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.hl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gt1', '540.hd1', '810.j1', '810.u1', '810.bw1'], 'contains': ['3240.ev1', '3240.ew1', '3240.ex1', '3240.fk1', '3240.he1', '3240.hj1', '3240.hq1', '4860.cf1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841004800, 19678982400, 224515, 448908243571, 462320328958], 'label': '77760.bo.1620.hl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.hl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.hl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055797
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.hm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gy1', '540.he1', '810.b1', '810.u1', '810.cb1'], 'contains': ['3240.fc1', '3240.fj1', '3240.fl2', '3240.fm1', '3240.gu1', '3240.he1', '3240.hx1', '4860.cg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [179012, 461841183480, 19678982400, 448908284158, 462320328958], 'label': '77760.bo.1620.hm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.hm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.hm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055798
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.hn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.ha1', '540.hb1', '540.hc1', '540.he1', '810.r1', '810.v1', '810.bt1'], 'contains': ['3240.fb1', '3240.ff1', '3240.fn1', '3240.fp1', '3240.gy1', '3240.hd1', '3240.hw1', '4860.cg1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841367555, 19679028004, 448908284158, 462320328958, 80787], 'label': '77760.bo.1620.hn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.hn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.hn1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055799
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ho1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.d2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.hf1', '540.hj1', '810.h1', '810.y1', '810.cb1'], 'contains': ['3240.ep1', '3240.es1', '3240.gu1', '3240.gv1', '3240.id1', '4860.ch1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [461841050163, 45363, 462320363997, 448908283914, 19679027763], 'label': '77760.bo.1620.ho1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.ho1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ho1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246055800
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.hp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.cg2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.hf1', '540.hg1', '540.hk1', '810.w1', '810.z1', '810.bt1'], 'contains': ['3240.fe1', '3240.fo1', '3240.gy1', '3240.hd1', '3240.ic1', '4860.ch1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [19679028004, 448908284158, 461841050404, 462320328958, 80787], 'label': '77760.bo.1620.hp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1620.hp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.hp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055801
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.hq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.hg1', '540.hl1', '810.j1', '810.x1', '810.cb1'], 'contains': ['3240.fi1', '3240.fq1', '3240.gz1', '3240.he1', '3240.id1', '4860.ch1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [461841004800, 19678982400, 143975, 448908284158, 462320328958], 'label': '77760.bo.1620.hq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '1620.hq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.hq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055802
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.hr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bs2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.hh1', '540.hi1', '540.hm1', '810.z1', '810.br1'], 'contains': ['3240.fu1', '3240.fw1', '3240.hf1', '3240.hg1', '3240.ic1', '4860.ci1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [448908278999, 462320323799, 19679028004, 461841050404, 80787], 'label': '77760.bo.1620.hr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '1620.hr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.hr1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246055803
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.hs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.v2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.hh1', '540.hn1', '810.j1', '810.y1', '810.bz1'], 'contains': ['3240.gc1', '3240.gh1', '3240.hj1', '3240.ho1', '3240.id1', '4860.ci1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [461841050163, 45363, 448908243571, 19679027763, 462320369015], 'label': '77760.bo.1620.hs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '1620.hs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.hs1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055804
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.n1', '24.f1', '36.d1', '36.h1', '36.l1'], 'contains': ['144.i1', '216.v1', '216.w1', '360.ff1', '432.l1', '720.ed1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [174879492215, 462320323891, 143975, 80787], 'label': '77760.bo.72.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.o1', 'subgroup_fusion': None, 'weyl_group': '1440.5849'}
  • id: 246055805
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.ht1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.hi1', '540.ho1', '810.ca1'], 'contains': ['3240.gg1', '3240.gi1', '3240.hk1', '3240.hp1', '3240.ie1', '4860.ci1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [461841004800, 462320288371, 19678982400, 143731, 448908243571], 'label': '77760.bo.1620.ht1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '1620.ht1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.ht1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055806
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.hu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.r1', '540.hj1', '540.hk1', '540.hl1', '810.i1', '810.k1', '810.bu1'], 'contains': ['3240.gw1', '3240.ha1', '3240.if1', '4860.ch1', '6480.dn1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [375138408958, 355462732800, 482630400, 462320328958, 87661244158], 'label': '77760.bo.1620.hu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '1620.hu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.hu1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055807
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1620.hv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.s1', '540.hm1', '540.hn1', '540.ho1', '810.k1', '810.bs1'], 'contains': ['3240.hh1', '3240.hl1', '3240.if1', '4860.ci1', '6480.do1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [461841004800, 462320288371, 19678982400, 448908243571, 262496505600], 'label': '77760.bo.1620.hv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '1620.hv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.hv1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246055808
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1728.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.a1', '864.a1', '864.b1', '864.c1', '864.e1', '864.g1', '864.h1', '864.i1'], 'contains': ['5184.a1', '5184.b1', '8640.a1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [18764570163, 80880, 80787], 'label': '77760.bo.1728.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '1728.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.a1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 246055809
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1728.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.a1', '864.d1', '864.f1', '864.j1'], 'contains': ['5184.a1', '5184.c1', '8640.b1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [18764605587, 80787, 179159], 'label': '77760.bo.1728.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '1728.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.b1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 246055810
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1944.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.a1', '648.a1', '648.d1', '648.f1', '972.a1'], 'contains': ['3888.a1', '3888.f1', '3888.g1', '9720.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [181146153005, 267841813805, 85805, 269202613805], 'label': '77760.bo.1944.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d1', 'old_label': '1944.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 246055811
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1944.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.b1', '648.b1', '648.e1', '648.g1', '972.a1'], 'contains': ['3888.a1', '3888.g1', '3888.h1', '9720.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [267841813805, 85805, 181146153355, 269202613805], 'label': '77760.bo.1944.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.a1', 'old_label': '1944.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 246055812
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1944.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.c1', '648.h1', '648.i1', '972.a1'], 'contains': ['3888.a1', '3888.b1', '3888.c1', '3888.d1', '3888.e1', '9720.k1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [1037980104, 5066, 18764663042, 143304], 'label': '77760.bo.1944.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.a1', 'old_label': '1944.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.c1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 246055813
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1944.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.f1', '648.j1', '648.m1', '648.o1', '972.a1'], 'contains': ['3888.d1', '3888.f1', '3888.h1', '9720.p1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [181146067893, 269202528693, 267841728693, 693], 'label': '77760.bo.1944.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.e1', 'old_label': '1944.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.d1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 246055814
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '1944.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.g1', '648.k1', '648.n1', '972.a1'], 'contains': ['3888.d1', '3888.g1', '9720.s1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [267841728693, 181146153355, 269202528693, 693], 'label': '77760.bo.1944.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.a1', 'old_label': '1944.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.e1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 246055815
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '72.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.o1', '24.f1', '36.m1'], 'contains': ['144.j1', '216.v1', '216.x1', '360.fi1', '432.n1', '720.ee1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [174879492215, 462320323891, 80787, 179159], 'label': '77760.bo.72.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.m1', 'old_label': '72.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.p1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 246055816
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.a1', '720.b1', '720.f1', '1080.a1', '1080.e1', '1080.bi1'], 'contains': ['4320.b1', '4320.w1', '4320.bn1', '6480.a1', '6480.b1', '6480.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [375138225118, 224515, 85946, 174436501946], 'label': '77760.bo.2160.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '2160.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246055817
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.b1', '720.b1', '720.g1', '1080.b1', '1080.e1', '1080.bj1'], 'contains': ['4320.b1', '4320.bb1', '4320.br1', '6480.a1', '6480.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [86155, 148, 375138172555, 188331091348], 'label': '77760.bo.2160.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '2160.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055818
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.b1', '720.h1', '1080.c1'], 'contains': ['4320.c1', '4320.be1', '4320.bw1', '6480.c1', '6480.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [174400490187, 85805, 83462400, 93449001575], 'label': '77760.bo.2160.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.a1', 'old_label': '2160.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055819
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.bh1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.b1', '720.i1', '720.j1', '1080.d1', '1080.f1', '1080.l1'], 'contains': ['4320.d1', '4320.bg1', '4320.bx1', '6480.b1', '6480.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [86155, 456053154955, 174400128000, 93448857600], 'label': '77760.bo.2160.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '2160.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055820
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.b1', '540.i1', '720.c1', '720.k1', '1080.e1', '1080.g1', '1080.bk1'], 'contains': ['4320.b1', '4320.bk1', '4320.cx1', '6480.e1', '6480.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [442637712120, 179012, 368392286010, 40442], 'label': '77760.bo.2160.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '2160.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.e1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055821
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.c1', '720.l1', '720.m1', '1080.f1', '1080.i1', '1080.j1', '1080.k1', '1080.m1'], 'contains': ['4320.d1', '4320.bm1', '4320.dg1', '6480.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [482849425, 219025, 193999276800, 280259700625], 'label': '77760.bo.2160.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '2160.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.f1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246055822
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.e1', '720.d1', '720.o1', '1080.b1', '1080.g1', '1080.bi1'], 'contains': ['4320.b1', '4320.bs1', '4320.ck1', '6480.g1', '6480.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [224515, 85946, 174436501946, 375138172555], 'label': '77760.bo.2160.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '2160.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.g1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055823
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.d1', '720.p1', '1080.c1'], 'contains': ['4320.c1', '4320.bv1', '4320.cp1', '6480.g1', '6480.j1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [456053154955, 174400271975, 85805, 93448857600], 'label': '77760.bo.2160.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.c1', 'old_label': '2160.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.h1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055824
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.n1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.d1', '720.n1', '720.q1', '1080.d1', '1080.i1', '1080.l1'], 'contains': ['4320.d1', '4320.bx1', '4320.cr1', '6480.g1', '6480.i1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [86155, 83462998, 174400128000, 93448857600], 'label': '77760.bo.2160.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.j1', 'old_label': '2160.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.i1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055825
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.f1', '720.d1', '720.r1', '1080.a1', '1080.g1', '1080.bj1'], 'contains': ['4320.b1', '4320.cc1', '4320.cu1', '6480.h1', '6480.i1', '6480.j1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [188331172080, 183845, 375138172205, 80880], 'label': '77760.bo.2160.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '2160.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.j1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055826
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '72.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.a1', '36.b1', '36.f1', '36.o1', '36.q1', '36.s1', '36.u1', '36.w1'], 'contains': ['216.a1', '432.p1', '720.et1', '1080.ig1'], 'core': '216.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [274511507904, 80880, 87181920000], 'label': '77760.bo.72.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '72.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.q1', 'subgroup_fusion': None, 'weyl_group': '1440.5842'}
  • id: 246055827
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.g1', '720.e1', '720.t1', '1080.a1', '1080.b1', '1080.bk1'], 'contains': ['4320.b1', '4320.dc1', '4320.dn1', '6480.k1', '6480.l1', '6480.m1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [442637757387, 143975, 40585, 368392188092], 'label': '77760.bo.2160.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '2160.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.k1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055830
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.w1', '720.x1', '1080.l1', '1080.m1'], 'contains': ['4320.d1', '4320.k1', '6480.n1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [280259567405, 193999277493, 85805, 693], 'label': '77760.bo.2160.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.e1', 'old_label': '2160.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.n1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 246055831
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.gb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.f1', '720.g1', '720.ba1', '1080.o1', '1080.o2', '1080.r1', '1080.r2', '1080.bx1'], 'contains': ['4320.e1', '4320.r1', '4320.bo1', '6480.a1', '6480.o1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [442641386187, 143975, 85805, 80787], 'label': '77760.bo.2160.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '2160.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.o1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055832
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.cd1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.t1', '720.f1', '720.i1', '720.y1', '1080.p1', '1080.u1', '1080.bl1'], 'contains': ['4320.f1', '4320.t1', '4320.bp1', '6480.b1', '6480.o1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [375138091561, 40349, 174436501946, 80787], 'label': '77760.bo.2160.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '2160.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.p1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055833
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.w1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.u1', '720.f1', '720.h1', '720.z1', '1080.q1'], 'contains': ['4320.g1', '4320.u1', '4320.bq1', '6480.c1', '6480.o1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [375138091561, 40349, 174436600173, 80787], 'label': '77760.bo.2160.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.f1', 'old_label': '2160.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.q1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055834
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.v1', '720.j1', '720.y1', '1080.n1', '1080.v1', '1080.bi1'], 'contains': ['4320.h1', '4320.w1', '4320.bs1', '6480.b1', '6480.p1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [375138091466, 174436501946, 5066, 80880], 'label': '77760.bo.2160.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '2160.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.r1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055835
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.ch1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.w1', '720.g1', '720.h1', '720.i1', '720.bb1', '1080.t1', '1080.u1', '1080.bm1'], 'contains': ['4320.f1', '4320.ba1', '4320.ca1', '6480.d1', '6480.o1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [188331171987, 86155, 375138172555, 80787], 'label': '77760.bo.2160.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '2160.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.s1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055836
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.x1', '720.j1', '720.bb1', '1080.s1', '1080.v1', '1080.bj1'], 'contains': ['4320.h1', '4320.bb1', '4320.cc1', '6480.d1', '6480.p1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [183845, 143975, 188331091200, 375138172555], 'label': '77760.bo.2160.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '2160.t1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.t1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055837
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.d1', '3.a1'], 'contains': ['12.b1', '12.h1', '12.n1', '18.j1', '18.l1', '36.l1', '60.r1', '90.bb1'], 'core': '12.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [93924311494, 462320323320, 143975, 80787, 143304], 'label': '77760.bo.6.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1', 'subgroup_fusion': None, 'weyl_group': '8640.t'}
  • id: 246055838
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '72.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1', '36.p1', '36.r1', '36.x1'], 'contains': ['216.a1', '432.q1', '720.ex1', '1080.ih1'], 'core': '216.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [87182282284, 274511462400, 179159], 'label': '77760.bo.72.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '72.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.r1', 'subgroup_fusion': None, 'weyl_group': '1440.5842'}
  • id: 246055839
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.a1', '720.k1', '720.bc1', '1080.r1', '1080.r2', '1080.w1', '1080.w2', '1080.x1', '1080.y1', '1080.z1', '1080.ba1', '1080.bb1', '1080.be1', '1080.by1'], 'contains': ['4320.e1', '4320.bh1', '4320.cw1', '6480.e1', '6480.q1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [183845, 80880, 80787, 274467916948], 'label': '77760.bo.2160.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '2160.u1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.u1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055840
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.e1', '540.bp1', '720.k1', '720.l1', '720.bd1', '1080.u1', '1080.bd1', '1080.bn1'], 'contains': ['4320.f1', '4320.bj1', '4320.da1', '6480.f1', '6480.q1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [113566924800, 5309, 88176216509, 80787], 'label': '77760.bo.2160.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '2160.v1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.v1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055841
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.f1', '540.bq1', '720.m1', '720.bd1', '1080.v1', '1080.bc1', '1080.bk1'], 'contains': ['4320.h1', '4320.bk1', '4320.dc1', '6480.f1', '6480.r1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [368392152509, 442637395200, 85805, 80880], 'label': '77760.bo.2160.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '2160.w1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.w1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055842
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.bd1', '720.n1', '720.be1', '1080.s1', '1080.bc1', '1080.bi1'], 'contains': ['4320.h1', '4320.bn1', '4320.ck1', '6480.g1', '6480.s1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [174436501946, 85805, 148, 375138172555], 'label': '77760.bo.2160.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '2160.x1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.x1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055843
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.z1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.bf1', '720.o1', '720.p1', '720.q1', '720.be1', '1080.t1', '1080.bd1', '1080.bl1'], 'contains': ['4320.f1', '4320.bp1', '4320.ce1', '6480.g1', '6480.t1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [40349, 174436501946, 375138172555, 80787], 'label': '77760.bo.2160.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '2160.y1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.y1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055844
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.be1', '720.n1', '720.bf1', '1080.n1', '1080.bc1', '1080.bj1'], 'contains': ['4320.h1', '4320.br1', '4320.cu1', '6480.i1', '6480.s1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [183845, 143975, 375138270474, 188331091200], 'label': '77760.bo.2160.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '2160.z1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.z1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055845
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gk1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.o1', '720.r1', '720.bh1', '1080.o1', '1080.o2', '1080.w1', '1080.w2', '1080.bx1'], 'contains': ['4320.e1', '4320.bz1', '4320.cf1', '6480.h1', '6480.t1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [442641386755, 5309, 143975, 80787], 'label': '77760.bo.2160.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '2160.ba1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ba1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055846
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.bb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.bh1', '720.q1', '720.r1', '720.bf1', '1080.p1', '1080.bd1', '1080.bm1'], 'contains': ['4320.f1', '4320.ca1', '4320.ch1', '6480.i1', '6480.t1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [183845, 188331171987, 375138172205, 80787], 'label': '77760.bo.2160.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.r1', 'old_label': '2160.bb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.bb1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055847
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.bi1', '720.p1', '720.r1', '720.bg1', '1080.q1'], 'contains': ['4320.g1', '4320.cb1', '4320.ci1', '6480.j1', '6480.t1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [442641386755, 277050, 442162067904, 80787], 'label': '77760.bo.2160.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.i1', 'old_label': '2160.bc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.bc1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055848
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.bk1', '720.s1', '720.bi1', '1080.n1', '1080.s1', '1080.bk1'], 'contains': ['4320.h1', '4320.cx1', '4320.dn1', '6480.l1', '6480.u1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [368392152811, 442637395200, 5066, 148], 'label': '77760.bo.2160.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '2160.bd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.bd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055849
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '80.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.a1', '40.b1', '40.f1'], 'contains': ['160.a1', '160.c1', '160.e1', '240.a1', '240.e1', '240.f1', '240.g1', '240.h1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 80, 'diagramx': None, 'generators': [183845, 456053074316, 93449001331, 143975, 174400173363, 80880, 80787], 'label': '77760.bo.80.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '80.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.a1', 'subgroup_fusion': None, 'weyl_group': '1296.2985'}
  • id: 246055850
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.b1', '720.t1', '720.bk1', '1080.o1', '1080.o2', '1080.bb1', '1080.by1'], 'contains': ['4320.e1', '4320.cz1', '4320.di1', '6480.k1', '6480.v1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [274468060348, 5309, 143975, 80787], 'label': '77760.bo.2160.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '2160.be1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.be1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055851
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.bm1', '720.t1', '720.u1', '720.v1', '720.bi1', '1080.p1', '1080.t1', '1080.bn1'], 'contains': ['4320.f1', '4320.da1', '4320.dk1', '6480.l1', '6480.v1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [442637475987, 85805, 80787, 368392188092], 'label': '77760.bo.2160.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '2160.bf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.bf1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055852
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.bn1', '720.t1', '720.u1', '720.bj1', '1080.q1'], 'contains': ['4320.g1', '4320.db1', '4320.dl1', '6480.m1', '6480.v1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [85805, 442637676988, 80787, 368392188092], 'label': '77760.bo.2160.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.q1', 'old_label': '2160.bg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.bg1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055853
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.bs1', '720.w1', '720.bl1', '1080.bi1', '1080.bj1', '1080.bk1'], 'contains': ['4320.b1', '4320.h1', '4320.n1', '6480.n1', '6480.w1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [143975, 194518339175, 85805, 143304], 'label': '77760.bo.2160.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '2160.bh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.bh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055854
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.br1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.bu1', '720.x1', '720.bl1', '1080.bl1', '1080.bm1', '1080.bn1'], 'contains': ['4320.f1', '4320.i1', '6480.n1', '6480.x1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [282215, 355419504452, 5309, 80787], 'label': '77760.bo.2160.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.r1', 'old_label': '2160.bi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.bi1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055855
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gk1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.y1', '720.z1', '720.ba1', '720.bb1', '1080.bo1', '1080.bo2', '1080.bp1', '1080.bp2', '1080.bx1'], 'contains': ['4320.a1', '4320.r1', '4320.bz1', '6480.o1', '6480.p1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [442641024148, 85805, 80880, 80787], 'label': '77760.bo.2160.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '2160.bj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.bj1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055856
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.c1', '720.bc1', '720.bd1', '1080.bp1', '1080.bp2', '1080.bq1', '1080.bq2', '1080.br1', '1080.bs1', '1080.bt1', '1080.bu1', '1080.bv1', '1080.bw1', '1080.by1'], 'contains': ['4320.a1', '4320.bh1', '4320.cz1', '6480.q1', '6480.r1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [85805, 80880, 80787, 274467916948], 'label': '77760.bo.2160.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '2160.bk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.bk1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055857
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gk1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.be1', '720.bf1', '720.bg1', '720.bh1', '1080.bo1', '1080.bo2', '1080.bq1', '1080.bq2', '1080.bx1'], 'contains': ['4320.a1', '4320.bo1', '4320.cf1', '6480.s1', '6480.t1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [442641386755, 85805, 80880, 80787], 'label': '77760.bo.2160.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '2160.bl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.bl1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055858
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.d1', '720.bi1', '720.bj1', '720.bk1', '1080.bo1', '1080.bo2', '1080.bv1', '1080.by1'], 'contains': ['4320.a1', '4320.cw1', '4320.di1', '6480.u1', '6480.v1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [274468060348, 85805, 80880, 80787], 'label': '77760.bo.2160.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '2160.bm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.bm1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055859
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.e1', '720.a1', '720.bl1', '1080.bx1', '1080.by1'], 'contains': ['4320.a1', '4320.e1', '4320.l1', '6480.w1', '6480.x1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [85805, 80880, 80787, 143304], 'label': '77760.bo.2160.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '720.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '2160.bn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.bn1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055860
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '80.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.b1', '40.c1', '40.d1', '40.e1', '40.g1'], 'contains': ['160.a1', '160.d1', '160.g1', '240.b1', '240.i1', '240.j1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [280259521949, 482635561, 143975, 193999455812, 85805, 80880, 80787], 'label': '77760.bo.80.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '80.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.b1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246055861
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.bo1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.cq1', '720.bm1', '720.bq1', '720.br1', '1080.bl1', '1080.bz1', '1080.cd1'], 'contains': ['4320.i1', '4320.t1', '4320.ce1', '6480.y1', '6480.z1', '6480.ba1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [224184, 174436559403, 80787, 375138086400], 'label': '77760.bo.2160.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '2160.bo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.bo1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246055862
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.bp1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.cr1', '720.bm1', '720.bs1', '720.bt1', '1080.bm1', '1080.ca1', '1080.cd1'], 'contains': ['4320.i1', '4320.ba1', '4320.ch1', '6480.y1', '6480.bb1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [188331315147, 178680, 80787, 375138086400], 'label': '77760.bo.2160.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.r1', 'old_label': '2160.bp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.bp1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055863
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.bm1', '720.bu1', '720.bw1', '1080.cb1'], 'contains': ['4320.j1', '4320.bd1', '4320.co1', '6480.ba1', '6480.bb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [83462998, 93448938387, 598, 174400173604], 'label': '77760.bo.2160.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.bu1', 'old_label': '2160.bq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.bq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055864
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.bi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.bm1', '720.bv1', '720.bx1', '1080.l1', '1080.cc1', '1080.ce1'], 'contains': ['4320.k1', '4320.bg1', '4320.cr1', '6480.z1', '6480.bb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [456053069398, 598, 174400128000, 93448857600], 'label': '77760.bo.2160.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.r1', 'old_label': '2160.br1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.br1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055865
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.j1', '540.cy1', '720.bn1', '720.by1', '720.bz1', '1080.bn1', '1080.cd1', '1080.cf1'], 'contains': ['4320.i1', '4320.bj1', '4320.dk1', '6480.bc1', '6480.bd1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [442637475987, 81237, 368392228437, 80787], 'label': '77760.bo.2160.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '2160.bs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.bs1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055866
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.bn1', '720.ca1', '720.cb1', '1080.m1', '1080.ce1', '1080.ch1', '1080.ci1', '1080.cj1'], 'contains': ['4320.k1', '4320.bm1', '4320.dr1', '6480.bd1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [280259481600, 482854584, 224184, 193999500984], 'label': '77760.bo.2160.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '2160.bt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.bt1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246055867
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.cu1', '720.bo1', '720.cc1', '1080.bl1', '1080.ca1', '1080.cf1'], 'contains': ['4320.i1', '4320.bp1', '6480.be1', '6480.bf1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [375138091561, 224184, 174436559403, 80787], 'label': '77760.bo.2160.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '2160.bu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.bu1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055868
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.bo1', '720.cd1', '1080.cb1'], 'contains': ['4320.j1', '4320.bu1', '6480.be1', '6480.bh1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [174400208787, 456053154955, 93448857600, 693], 'label': '77760.bo.2160.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.cb1', 'old_label': '2160.bv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.bv1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055869
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.bo1', '720.ce1', '1080.l1', '1080.cc1', '1080.ch1'], 'contains': ['4320.k1', '4320.bx1', '6480.be1', '6480.bg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [83548555, 174400128000, 93448857600, 693], 'label': '77760.bo.2160.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.j1', 'old_label': '2160.bw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.bw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055870
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.cv1', '720.bo1', '720.cf1', '1080.bm1', '1080.bz1', '1080.cf1'], 'contains': ['4320.i1', '4320.ca1', '6480.bf1', '6480.bg1', '6480.bh1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [178680, 442162022400, 442641109705, 80787], 'label': '77760.bo.2160.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.r1', 'old_label': '2160.bx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.bx1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055871
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '80.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.a1', '40.c1', '40.f1'], 'contains': ['160.a1', '160.e1', '160.f1', '240.c1', '240.k1', '240.l1', '240.m1', '240.n1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 80, 'diagramx': None, 'generators': [93449001331, 83543730, 143975, 174400173363, 85805, 80880, 80787], 'label': '77760.bo.80.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '80.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.c1', 'subgroup_fusion': None, 'weyl_group': '1296.2985'}
  • id: 246055872
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.cw1', '720.bp1', '720.cg1', '1080.bn1', '1080.bz1', '1080.ca1'], 'contains': ['4320.i1', '4320.da1', '6480.bi1', '6480.bj1', '6480.bk1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [442637475987, 80787, 368392188092, 693], 'label': '77760.bo.2160.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '2160.by1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.by1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055873
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.bp1', '720.ch1', '1080.cb1'], 'contains': ['4320.j1', '4320.de1', '6480.bj1', '6480.bk1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [280259562387, 482849425, 193999455627, 143304], 'label': '77760.bo.2160.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.cb1', 'old_label': '2160.bz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.bz1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055874
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.bp1', '720.ci1', '1080.m1', '1080.cc1'], 'contains': ['4320.k1', '4320.dg1', '6480.bj1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [280259481600, 482849425, 193999420104, 143304], 'label': '77760.bo.2160.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.e1', 'old_label': '2160.ca1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ca1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246055875
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.ga1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.bq1', '720.bs1', '720.cj1', '1080.bx1', '1080.ck1', '1080.ck2', '1080.cn1', '1080.cn2'], 'contains': ['4320.l1', '4320.r1', '4320.cf1', '6480.y1', '6480.bl1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [442641024148, 80880, 80787, 143304], 'label': '77760.bo.2160.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '2160.cb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.cb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055876
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.ga1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.br1', '720.bt1', '720.cj1', '1080.co1', '1080.co2'], 'contains': ['4320.m1', '4320.s1', '4320.cg1', '6480.y1', '6480.bm1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [442641386284, 80787, 143304, 179159], 'label': '77760.bo.2160.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '2160.cc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.cc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246055877
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.p1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.dl1', '720.bq1', '720.bv1', '1080.bi1', '1080.cl1', '1080.cq1'], 'contains': ['4320.n1', '4320.w1', '4320.ck1', '6480.z1', '6480.bl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [224184, 224515, 174436640184, 375138310915], 'label': '77760.bo.2160.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '2160.cd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.cd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055878
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.t1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.dm1', '720.bq1', '720.bu1', '1080.cm1'], 'contains': ['4320.o1', '4320.x1', '4320.cl1', '6480.ba1', '6480.bl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [442641386187, 143975, 519235320, 143304], 'label': '77760.bo.2160.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.bz1', 'old_label': '2160.ce1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ce1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055879
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.dn1', '720.br1', '720.bx1', '1080.cr1'], 'contains': ['4320.p1', '4320.y1', '4320.cm1', '6480.z1', '6480.bm1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [442641305544, 519199944, 143731, 143304], 'label': '77760.bo.2160.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ce1', 'old_label': '2160.cf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.cf1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055880
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.do1', '720.br1', '720.bw1'], 'contains': ['4320.q1', '4320.z1', '4320.cn1', '6480.ba1', '6480.bm1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [224184, 375138311012, 174436559403, 224612], 'label': '77760.bo.2160.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '720.br1', 'old_label': '2160.cg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.cg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246055881
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.s1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.dp1', '720.bs1', '720.bu1', '720.bv1', '1080.bj1', '1080.cp1', '1080.cq1'], 'contains': ['4320.n1', '4320.bb1', '4320.cu1', '6480.bb1', '6480.bl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [179012, 188331269880, 178680, 375138265412], 'label': '77760.bo.2160.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '2160.ch1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ch1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055882
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '80.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.a1', '40.g1'], 'contains': ['160.a1', '160.g1', '160.h1', '240.d1', '240.o1', '240.p1', '240.q1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [280259521949, 143975, 193999455812, 482768881, 85805, 80880, 80787], 'label': '77760.bo.80.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '80.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.d1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246055883
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.dq1', '720.bt1', '720.bw1', '720.bx1', '1080.cr1'], 'contains': ['4320.p1', '4320.bc1', '4320.cv1', '6480.bb1', '6480.bm1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [375138265559, 188331269880, 178680, 179159], 'label': '77760.bo.2160.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.x1', 'old_label': '2160.ci1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ci1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055884
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.f1', '720.by1', '720.ck1', '1080.by1', '1080.cn1', '1080.cn2', '1080.cs1', '1080.cs2', '1080.ct1', '1080.cu1', '1080.cv1', '1080.cw1', '1080.cx1', '1080.db1'], 'contains': ['4320.l1', '4320.bh1', '4320.di1', '6480.bc1', '6480.bn1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [80880, 80787, 274467916948, 143304], 'label': '77760.bo.2160.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '2160.cj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.cj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055885
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.g1', '720.bz1', '720.ck1', '1080.co1', '1080.co2', '1080.cy1', '1080.cz1', '1080.dc1'], 'contains': ['4320.m1', '4320.bi1', '4320.dj1', '6480.bc1', '6480.bo1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [274467962404, 80787, 143304, 179159], 'label': '77760.bo.2160.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '2160.ck1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ck1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246055886
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.n1', '540.eg1', '720.by1', '720.ca1', '1080.bk1', '1080.cq1', '1080.da1'], 'contains': ['4320.n1', '4320.bk1', '4320.dn1', '6480.bd1', '6480.bn1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [113566924800, 179012, 178680, 88176211650], 'label': '77760.bo.2160.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '2160.cl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.cl1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055887
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.o1', '540.eh1', '720.bz1', '720.cb1', '1080.cr1'], 'contains': ['4320.p1', '4320.bl1', '4320.do1', '6480.bd1', '6480.bo1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [143731, 368392147650, 442637676744, 143304], 'label': '77760.bo.2160.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ce1', 'old_label': '2160.cm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.cm1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055888
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.dw1', '720.cc1', '720.cd1', '720.ce1', '1080.bi1', '1080.cp1', '1080.da1'], 'contains': ['4320.n1', '4320.bn1', '4320.bs1', '6480.be1', '6480.bp1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [224184, 375138225118, 224515, 174436640184], 'label': '77760.bo.2160.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '2160.cn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.cn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055889
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gk1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.cc1', '720.cf1', '720.cl1', '1080.bx1', '1080.ck1', '1080.ck2', '1080.cs1', '1080.cs2'], 'contains': ['4320.l1', '4320.bo1', '4320.bz1', '6480.bf1', '6480.bp1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [178680, 442641300482, 143975, 80787], 'label': '77760.bo.2160.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '2160.co1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.co1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055890
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.dy1', '720.ce1', '720.cf1', '1080.bj1', '1080.cl1', '1080.da1'], 'contains': ['4320.n1', '4320.br1', '4320.cc1', '6480.bg1', '6480.bp1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [188331234504, 143975, 375138270474, 143304], 'label': '77760.bo.2160.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '2160.cp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.cp1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055891
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.dz1', '720.cd1', '720.cf1', '1080.cm1'], 'contains': ['4320.o1', '4320.bt1', '4320.cd1', '6480.bh1', '6480.bp1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [179012, 178680, 442641300482, 442162103187], 'label': '77760.bo.2160.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.cb1', 'old_label': '2160.cq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.cq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055892
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.h1', '720.cg1', '720.cm1', '1080.by1', '1080.ck1', '1080.ck2', '1080.ct1'], 'contains': ['4320.l1', '4320.cw1', '4320.cz1', '6480.bi1', '6480.bq1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [274468002505, 80880, 80787, 143304], 'label': '77760.bo.2160.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '2160.cr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.cr1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055893
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '80.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.f1', '40.g1'], 'contains': ['160.a1', '160.b1', '240.r1', '240.s1'], 'core': '720.a1', 'coset_action_label': None, 'count': 10, 'diagramx': None, 'generators': [193999357894, 280259521949, 143975, 85805, 80880, 80787, 143304], 'label': '77760.bo.80.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '80.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.e1', 'subgroup_fusion': None, 'weyl_group': '864.2470'}
  • id: 246055894
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.ec1', '720.cg1', '720.ch1', '720.ci1', '1080.bk1', '1080.cl1', '1080.cp1'], 'contains': ['4320.n1', '4320.cx1', '4320.dc1', '6480.bj1', '6480.bq1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [442637757387, 143975, 368392188092, 143304], 'label': '77760.bo.2160.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '2160.cs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.cs1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055895
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.ed1', '720.cg1', '720.ch1', '1080.cm1'], 'contains': ['4320.o1', '4320.cy1', '4320.dd1', '6480.bk1', '6480.bq1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [113567005587, 88176252092, 143975, 143304], 'label': '77760.bo.2160.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.cm1', 'old_label': '2160.ct1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ct1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055896
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.ec1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.cn1', '720.co1', '720.cp1', '720.cx1', '1080.r1', '1080.bo1', '1080.ck1', '1080.dh2', '1080.dh4', '1080.di1', '1080.di2'], 'contains': ['4320.r1', '4320.bo1', '4320.cw1', '6480.br1', '6480.bs1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [87182277125, 143975, 375138270474, 80787], 'label': '77760.bo.2160.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bj1', 'old_label': '2160.cu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.cu1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055897
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.cu2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gi1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.cp2', '1080.r2', '1080.bo2', '1080.ck2', '1080.dh1', '1080.dh3', '1080.di1', '1080.di2'], 'contains': ['4320.r1', '4320.bo1', '4320.cw1', '6480.br2', '6480.bs2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [442641386187, 448908283441, 143975, 80787], 'label': '77760.bo.2160.cu2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '2160.cu2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.cu2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055898
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.fe1', '720.cn1', '720.cz1', '1080.e1', '1080.n1', '1080.cl1'], 'contains': ['4320.w1', '4320.br1', '4320.cx1', '6480.br1', '6480.bu1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [518918400, 442641024148, 997961035, 148], 'label': '77760.bo.2160.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '2160.cv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.cv1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055899
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.ff1', '720.cn1', '720.cy1', '1080.cm1'], 'contains': ['4320.x1', '4320.bt1', '4320.cy1', '6480.br1', '6480.bv1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [368871287518, 174436496787, 224515, 375138310915], 'label': '77760.bo.2160.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.cm1', 'old_label': '2160.cw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.cw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055900
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.cp1', '720.cq1', '720.da1', '1080.o1', '1080.bp1', '1080.ck1', '1080.dh1', '1080.dh4', '1080.dk1', '1080.dk2'], 'contains': ['4320.r1', '4320.bz1', '4320.cz1', '6480.bs1', '6480.bt1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [442641386187, 143975, 443120066492, 80787], 'label': '77760.bo.2160.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.x1', 'old_label': '2160.cx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.cx1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055901
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.cx2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.cp2', '1080.o2', '1080.bp2', '1080.ck2', '1080.dh2', '1080.dh3', '1080.dk1', '1080.dk2'], 'contains': ['4320.r1', '4320.bz1', '4320.cz1', '6480.bs2', '6480.bt2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 442641301050, 80787, 448908278520], 'label': '77760.bo.2160.cx2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '2160.cx2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.cx2', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055902
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.fh1', '720.cn1', '720.cq1', '720.dc1', '1080.p1', '1080.u1', '1080.bz1'], 'contains': ['4320.t1', '4320.ca1', '4320.da1', '6480.bs1', '6480.bu1', '6480.bv1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [174436496787, 368871153961, 80787, 375138086400], 'label': '77760.bo.2160.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '2160.cy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.cy1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055903
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.fi1', '720.co1', '720.cq1', '720.db1', '1080.q1'], 'contains': ['4320.u1', '4320.cb1', '4320.db1', '6480.bs1', '6480.bw1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [368871234955, 174436595012, 80787, 375138086400], 'label': '77760.bo.2160.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ba1', 'old_label': '2160.cz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.cz1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055904
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '80.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.f1', '40.h1', '40.i1'], 'contains': ['160.b1', '160.c1', '160.f1', '240.t1', '240.u1', '240.z1', '240.ba1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [93449001331, 143975, 174400173363, 456053150130, 80880, 80787, 143304], 'label': '77760.bo.80.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '80.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.f1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 246055905
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.fj1', '720.cq1', '720.de1', '1080.a1', '1080.v1', '1080.cl1'], 'contains': ['4320.w1', '4320.cc1', '4320.dc1', '6480.bt1', '6480.bu1', '6480.bw1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [518918400, 442641024148, 148, 997960349], 'label': '77760.bo.2160.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '2160.da1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.da1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055906
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.fk1', '720.cq1', '720.dd1', '1080.cm1'], 'contains': ['4320.x1', '4320.cd1', '4320.dd1', '6480.bt1', '6480.bv1', '6480.bw1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [368871153961, 174436416243, 80880, 375138086400], 'label': '77760.bo.2160.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.cm1', 'old_label': '2160.db1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.db1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055907
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.cr1', '720.cs1', '720.ct1', '720.df1', '1080.o1', '1080.bo1', '1080.cn1', '1080.dh1', '1080.dh2', '1080.dm1', '1080.dm2'], 'contains': ['4320.r1', '4320.cf1', '4320.di1', '6480.bx1', '6480.by1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [87182202116, 80880, 80787, 375138086400], 'label': '77760.bo.2160.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bj1', 'old_label': '2160.dc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.dc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055908
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.dc2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gh1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.ct2', '1080.o2', '1080.bo2', '1080.cn2', '1080.dh3', '1080.dh4', '1080.dm1', '1080.dm2'], 'contains': ['4320.r1', '4320.cf1', '4320.di1', '6480.bx2', '6480.by2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [442641386755, 143975, 80787, 448908278520], 'label': '77760.bo.2160.dc2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '2160.dc2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.dc2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056003
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.fk1', '720.fo1', '1080.c1'], 'contains': ['4320.bv1', '4320.bw1', '4320.dp1', '6480.ee1', '6480.ef1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [180587456184, 174400173504, 456053073961, 93448857600], 'label': '77760.bo.2160.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.c1', 'old_label': '2160.gb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.gb1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055909
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.ct1', '720.cu1', '720.cv1', '720.dg1', '1080.co1', '1080.dn1', '1080.dn2'], 'contains': ['4320.s1', '4320.cg1', '4320.dj1', '6480.bx1', '6480.bz1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [442641386284, 443120071554, 80787, 179159], 'label': '77760.bo.2160.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.dk1', 'old_label': '2160.dd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.dd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246055910
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.dd2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.ct2', '1080.co2', '1080.dn1', '1080.dn2'], 'contains': ['4320.s1', '4320.cg1', '4320.dj1', '6480.bx2', '6480.bz2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [442641386755, 448908278667, 80787, 179159], 'label': '77760.bo.2160.dd2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '2160.dd2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.dd2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246055911
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.fn1', '720.cr1', '720.cu1', '720.dj1', '1080.p1', '1080.cd1'], 'contains': ['4320.t1', '4320.ch1', '4320.dk1', '6480.bx1', '6480.ca1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [174436496787, 368871230130, 80787, 375138086400], 'label': '77760.bo.2160.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '2160.de1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.de1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055912
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.fo1', '720.cr1', '720.cs1', '720.cv1', '720.dh1', '1080.q1'], 'contains': ['4320.u1', '4320.ci1', '4320.dl1', '6480.bx1', '6480.cb1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [174436595012, 368871230130, 80787, 375138086400], 'label': '77760.bo.2160.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.q1', 'old_label': '2160.df1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.df1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055913
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.fp1', '720.cs1', '720.cu1', '720.cv1', '720.di1'], 'contains': ['4320.v1', '4320.cj1', '4320.dm1', '6480.bx1', '6480.cc1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [442641024000, 997965813, 80787, 519235228], 'label': '77760.bo.2160.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2160.dg1', 'old_label': '2160.dg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.dg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246055914
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.fq1', '720.cr1', '720.dk1', '1080.a1', '1080.n1', '1080.cq1'], 'contains': ['4320.w1', '4320.cu1', '4320.dn1', '6480.by1', '6480.ca1', '6480.cb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [997920598, 224515, 442641305788, 519200188], 'label': '77760.bo.2160.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '2160.dh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.dh1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055915
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '80.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.g1', '40.i1', '40.j1', '40.k1', '40.l1'], 'contains': ['160.b1', '160.d1', '160.h1', '240.v1', '240.w1', '240.bb1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 10, 'diagramx': None, 'generators': [482808988, 193999357894, 143975, 280259527104, 80880, 80787, 143304], 'label': '77760.bo.80.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '80.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.g1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246055916
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.fr1', '720.cu1', '720.dl1', '1080.cr1'], 'contains': ['4320.y1', '4320.cv1', '4320.do1', '6480.bz1', '6480.ca1', '6480.cc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [997920598, 442641386284, 519280684, 179159], 'label': '77760.bo.2160.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ce1', 'old_label': '2160.di1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.di1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055917
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.ee1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.cw1', '720.dm1', '1080.r1', '1080.bp1', '1080.cn1', '1080.di2', '1080.dj1', '1080.dk2', '1080.dl1', '1080.dm2', '1080.do1', '1080.dq1', '1080.dr1', '1080.ds1', '1080.ea1', '1080.ec1', '1080.ee1'], 'contains': ['4320.r1', '4320.bh1', '6480.cd1', '6480.ce1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [442641386187, 443120250115, 143975, 80787], 'label': '77760.bo.2160.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '2160.dj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.dj1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055918
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.dj2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.fy1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.cw2', '1080.r2', '1080.bp2', '1080.cn2', '1080.di1', '1080.dk1', '1080.dm1', '1080.du1', '1080.dv1', '1080.dw1', '1080.dx1', '1080.ee1'], 'contains': ['4320.r1', '4320.bh1', '6480.cd2', '6480.ce2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [442641024148, 448908007104, 80880, 80787], 'label': '77760.bo.2160.dj2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '2160.dj2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.dj2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055919
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.ef1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.cw1', '720.dn1', '1080.co1', '1080.dn2', '1080.dp1', '1080.dt1', '1080.eb1', '1080.ed1', '1080.ef1'], 'contains': ['4320.s1', '4320.bi1', '6480.cd1', '6480.cf1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [443120204759, 442641386284, 80787, 179159], 'label': '77760.bo.2160.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bi1', 'old_label': '2160.dk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.dk1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055920
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.dk2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.fz1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.cw2', '1080.co2', '1080.dn1', '1080.dy1', '1080.dz1', '1080.ef1'], 'contains': ['4320.s1', '4320.bi1', '6480.cd2', '6480.cf2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [442641386284, 448908278667, 80787, 179159], 'label': '77760.bo.2160.dk2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bi1', 'old_label': '2160.dk2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.dk2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246055921
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.fs1', '720.cx1', '720.cy1', '720.cz1', '1080.e1', '1080.s1', '1080.cp1'], 'contains': ['4320.bb1', '4320.bn1', '4320.cx1', '6480.br1', '6480.cg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [174436416243, 148, 368871149043, 375138172555], 'label': '77760.bo.2160.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '2160.dl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.dl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055922
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.ft1', '720.cx1', '720.da1', '720.db1', '720.dc1', '1080.t1', '1080.u1', '1080.ca1'], 'contains': ['4320.ba1', '4320.bp1', '4320.da1', '6480.bs1', '6480.cg1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [518964004, 998000787, 442641109705, 80787], 'label': '77760.bo.2160.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '2160.dm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.dm1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055923
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.fu1', '720.da1', '720.dd1', '720.de1', '1080.b1', '1080.v1', '1080.cp1'], 'contains': ['4320.bb1', '4320.bs1', '4320.dc1', '6480.bt1', '6480.cg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [368871292775, 143975, 375138172555, 174436416000], 'label': '77760.bo.2160.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '2160.dn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.dn1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055924
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.cy1', '720.dc1', '720.dd1', '1080.cb1'], 'contains': ['4320.bd1', '4320.bu1', '4320.de1', '6480.bv1', '6480.cg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [180587317946, 174400208787, 93448938387, 83467561], 'label': '77760.bo.2160.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.cb1', 'old_label': '2160.do1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.do1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055925
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.db1', '720.dd1', '720.de1', '1080.c1'], 'contains': ['4320.be1', '4320.bv1', '4320.df1', '6480.bw1', '6480.cg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [174400173363, 180587272442, 83467561, 93448902963], 'label': '77760.bo.2160.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.c1', 'old_label': '2160.dp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.dp1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055926
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '80.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.f1', '40.h1', '40.j1'], 'contains': ['160.b1', '160.e1', '240.x1', '240.bc1', '240.bd1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [93449001331, 83467916, 143975, 174400173363, 80880, 80787, 143304], 'label': '77760.bo.80.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '80.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.h1', 'subgroup_fusion': None, 'weyl_group': '1296.2985'}
  • id: 246055927
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.w1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.cz1', '720.dc1', '720.de1', '1080.d1', '1080.f1', '1080.cc1'], 'contains': ['4320.bg1', '4320.bx1', '4320.dg1', '6480.bu1', '6480.cg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [456053068800, 174400128000, 180587272349, 93448857600], 'label': '77760.bo.2160.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '2160.dq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.dq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056004
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.fk1', '720.fp1', '1080.d1', '1080.ch1'], 'contains': ['4320.bx1', '4320.dr1', '6480.ee1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [180587456184, 174400128000, 456053073961, 93448857600], 'label': '77760.bo.2160.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.j1', 'old_label': '2160.gc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.gc1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055928
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.fv1', '720.df1', '720.dg1', '720.dh1', '720.di1', '720.dj1', '1080.t1', '1080.cd1'], 'contains': ['4320.ba1', '4320.ce1', '4320.dk1', '6480.bx1', '6480.ch1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [518964004, 442641386755, 998000787, 80787], 'label': '77760.bo.2160.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '2160.dr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.dr1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055929
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.fw1', '720.df1', '720.dk1', '1080.b1', '1080.s1', '1080.cq1'], 'contains': ['4320.bb1', '4320.ck1', '4320.dn1', '6480.by1', '6480.ch1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [518918400, 45363, 998000644, 442641341252], 'label': '77760.bo.2160.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '2160.ds1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ds1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055930
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.fx1', '720.dg1', '720.dl1', '1080.cr1'], 'contains': ['4320.bc1', '4320.cm1', '4320.do1', '6480.bz1', '6480.ch1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [375138087093, 368871373412, 174436416000, 224612], 'label': '77760.bo.2160.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ce1', 'old_label': '2160.dt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.dt1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055931
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.dh1', '720.dk1', '1080.c1'], 'contains': ['4320.be1', '4320.cp1', '4320.dp1', '6480.cb1', '6480.ch1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [180587232598, 456053069398, 174400352515, 93448857600], 'label': '77760.bo.2160.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.i1', 'old_label': '2160.du1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.du1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055932
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.di1', '720.dl1'], 'contains': ['4320.bf1', '4320.cq1', '4320.dq1', '6480.cc1', '6480.ch1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [180587456184, 174400352612, 93449174667, 83462400], 'label': '77760.bo.2160.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '720.di1', 'old_label': '2160.dv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.dv1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055933
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.dj1', '720.dk1', '720.dl1', '1080.d1', '1080.ce1'], 'contains': ['4320.bg1', '4320.cr1', '4320.dr1', '6480.ca1', '6480.ch1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [180587232598, 456053069398, 174400128000, 93448857600], 'label': '77760.bo.2160.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.r1', 'old_label': '2160.dw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.dw1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055934
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.cj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.p1', '540.ga1', '720.dm1', '720.dn1', '720.do1', '1080.u1', '1080.cd1'], 'contains': ['4320.t1', '4320.ba1', '4320.bj1', '6480.cd1', '6480.ci1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [518964004, 442641024000, 998000787, 80787], 'label': '77760.bo.2160.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '2160.dx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.dx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055935
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.q1', '540.gb1', '720.dm1', '720.dp1', '1080.e1', '1080.v1', '1080.cq1'], 'contains': ['4320.w1', '4320.bb1', '4320.bk1', '6480.ce1', '6480.ci1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [442641386187, 519280587, 143975, 998063975], 'label': '77760.bo.2160.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '2160.dy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.dy1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055936
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.r1', '540.gc1', '720.dn1', '720.dq1', '1080.cr1'], 'contains': ['4320.y1', '4320.bc1', '4320.bl1', '6480.cf1', '6480.ci1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [375138265559, 368871327959, 174436416000, 179159], 'label': '77760.bo.2160.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ce1', 'old_label': '2160.dz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.dz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055937
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '80.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.g1', '40.h1'], 'contains': ['160.b1', '160.g1', '240.y1', '240.be1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 10, 'diagramx': None, 'generators': [193999357894, 143975, 280259527104, 482768881, 80880, 80787, 143304], 'label': '77760.bo.80.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '80.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.i1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246055938
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.do1', '720.dp1', '720.dq1', '1080.f1', '1080.ce1', '1080.eq1', '1080.er1', '1080.es1'], 'contains': ['4320.bg1', '4320.bm1', '6480.ci1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [456053068800, 174400128000, 180587232000, 93448857600], 'label': '77760.bo.2160.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '2160.ea1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ea1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246055939
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.ec1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.dr1', '720.eb1', '1080.r1', '1080.bq1', '1080.cs1', '1080.di1', '1080.dj1', '1080.et2', '1080.eu1', '1080.ev1', '1080.ew1', '1080.ex1', '1080.fc1', '1080.fm2', '1080.fn1', '1080.gj1', '1080.gm1'], 'contains': ['4320.bh1', '4320.bo1', '6480.cj1', '6480.ck1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [375138172555, 80880, 80787, 87182000787], 'label': '77760.bo.2160.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '2160.eb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.eb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055940
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.eb2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.dr2', '1080.r2', '1080.bq2', '1080.cs2', '1080.di2', '1080.et1', '1080.ey1', '1080.ez1', '1080.fa1', '1080.fb1', '1080.fm1', '1080.gm1'], 'contains': ['4320.bh1', '4320.bo1', '6480.cj2', '6480.ck2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [442641300958, 80880, 80787, 448908283914], 'label': '77760.bo.2160.eb2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '2160.eb2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.eb2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055941
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.dr1', '720.ec1', '1080.w1', '1080.bp1', '1080.cs1', '1080.dk1', '1080.dl1', '1080.fd2', '1080.fe1', '1080.ff1', '1080.fg1', '1080.fh1', '1080.fm1', '1080.fn1', '1080.fo1', '1080.gq1', '1080.gv1'], 'contains': ['4320.bh1', '4320.bz1', '6480.ck1', '6480.cl1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [443120250115, 143975, 442641301050, 80787], 'label': '77760.bo.2160.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '2160.ec1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ec1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246055942
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ec2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.dr2', '1080.w2', '1080.bp2', '1080.cs2', '1080.dk2', '1080.fd1', '1080.fi1', '1080.fj1', '1080.fk1', '1080.fl1', '1080.fm2', '1080.gv1'], 'contains': ['4320.bh1', '4320.bz1', '6480.ck2', '6480.cl2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [143975, 448908284158, 442641301050, 80787], 'label': '77760.bo.2160.ec2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '2160.ec2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ec2', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246055943
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.ds1', '720.ed1', '1080.w1', '1080.bq1', '1080.cn1', '1080.dm1', '1080.do1', '1080.et1', '1080.eu1', '1080.fd1', '1080.fe1', '1080.fp1', '1080.fq1', '1080.fr1', '1080.fz1', '1080.gx1', '1080.hc1'], 'contains': ['4320.bh1', '4320.cf1', '6480.cm1', '6480.cn1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [375138087093, 143975, 87182201788, 80787], 'label': '77760.bo.2160.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '2160.ed1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ed1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055944
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ed2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.ds2', '1080.w2', '1080.bq2', '1080.cn2', '1080.dm2', '1080.et2', '1080.fd2', '1080.ft1', '1080.fu1', '1080.fv1', '1080.fw1', '1080.hc1'], 'contains': ['4320.bh1', '4320.cf1', '6480.cm2', '6480.cn2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [448908278999, 442641386852, 143975, 80787], 'label': '77760.bo.2160.ed2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '2160.ed2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ed2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055945
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.ds1', '720.ee1', '1080.co1', '1080.dn1', '1080.dp1', '1080.fs1', '1080.ga1', '1080.gy1', '1080.hd1'], 'contains': ['4320.bi1', '4320.cg1', '6480.cm1', '6480.co1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [443120204759, 442641386755, 80787, 179159], 'label': '77760.bo.2160.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '2160.ee1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ee1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055946
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ee2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.ds2', '1080.co2', '1080.dn2', '1080.fx1', '1080.fy1', '1080.hd1'], 'contains': ['4320.bi1', '4320.cg1', '6480.cm2', '6480.co2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [448908278999, 442641386852, 80787, 179159], 'label': '77760.bo.2160.ee2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '2160.ee2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ee2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246055947
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.ec1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.dt1', '1080.be1', '1080.bv1', '1080.ct1', '1080.di1', '1080.di2', '1080.dq1', '1080.ev1', '1080.fd1', '1080.fd2', '1080.ff1', '1080.fp1', '1080.gb1', '1080.gc1', '1080.ge1', '1080.hk1'], 'contains': ['4320.bh1', '4320.cw1', '6480.cp1', '6480.cq1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [442680946109, 355499240157, 143975, 80787], 'label': '77760.bo.2160.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '2160.ef1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ef1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055948
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': ['38880.h1', '38880.g1', '38880.b1', '38880.a1', '38880.f1', '38880.e1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.c1', '4.d1', '6.a1', '6.b1', '12.e1', '20.b1', '30.c1'], 'core': '2.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [183845, 143975, 462320328958, 93924236159, 80880, 80787], 'label': '77760.bo.2.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.c1', '4.d1', '6.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '77760.bo', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '77760.bo'}
  • id: 246055949
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1'], 'contains': ['12.i1', '12.l1', '12.o1', '18.j1', '18.m1', '36.m1', '60.s1', '90.bc1'], 'core': '36.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [93924311494, 224184, 462320323467, 80787, 179159], 'label': '77760.bo.6.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '6.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
  • id: 246055950
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '80.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.a1', '40.b1', '40.h1'], 'contains': ['160.c1', '160.e1', '160.g1', '240.bf1', '240.bh1', '240.bi1', '240.bj1', '240.bk1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 80, 'diagramx': None, 'generators': [83601118, 93449001331, 143975, 174400173363, 180587272349, 80880, 80787], 'label': '77760.bo.80.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '80.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.j1', 'subgroup_fusion': None, 'weyl_group': '3888.ik'}
  • id: 246055951
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.dt1', '1080.bb1', '1080.bw1', '1080.ct1', '1080.dk1', '1080.dk2', '1080.dr1', '1080.et1', '1080.et2', '1080.ew1', '1080.fg1', '1080.fq1', '1080.gd1', '1080.ge1', '1080.gf1', '1080.hn1'], 'contains': ['4320.bh1', '4320.cz1', '6480.cq1', '6480.cr1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 274468135825, 268244605587, 80787], 'label': '77760.bo.2160.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '2160.eg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.eg1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246055952
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.du1', '1080.bb1', '1080.bv1', '1080.db1', '1080.dm1', '1080.dm2', '1080.ds1', '1080.ex1', '1080.fh1', '1080.fm1', '1080.fm2', '1080.fr1', '1080.gb1', '1080.gd1', '1080.gg1', '1080.hs1'], 'contains': ['4320.bh1', '4320.di1', '6480.cs1', '6480.ct1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [274468060348, 143975, 268244605587, 80787], 'label': '77760.bo.2160.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '2160.eh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.eh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055953
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.du1', '1080.dc1', '1080.dn1', '1080.dn2', '1080.dt1', '1080.fs1', '1080.gh1', '1080.ht1'], 'contains': ['4320.bi1', '4320.dj1', '6480.cs1', '6480.cu1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [274468060348, 268244605587, 80787, 179159], 'label': '77760.bo.2160.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '2160.ei1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ei1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055954
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.du1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.i1', '720.dv1', '1080.x1', '1080.br1', '1080.cu1', '1080.du1', '1080.ea1', '1080.ev1', '1080.ey1', '1080.fg1', '1080.fi1', '1080.fr1', '1080.ft1'], 'contains': ['4320.bh1', '6480.cv1', '6480.db1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [443120071204, 267845402163, 80880, 80787], 'label': '77760.bo.2160.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '2160.ej1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ej1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055955
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.du1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.ca1', '720.dw1', '1080.y1', '1080.bs1', '1080.cv1', '1080.du1', '1080.ec1', '1080.ez1', '1080.fc1', '1080.fj1', '1080.fo1', '1080.fu1', '1080.fz1', '1080.gc1', '1080.gf1', '1080.gg1', '1080.hz1'], 'contains': ['4320.bh1', '6480.cw1', '6480.dc1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [482676004, 88695175204, 143975, 80787], 'label': '77760.bo.2160.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '2160.ek1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ek1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055956
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.cb1', '720.dx1', '1080.z1', '1080.bt1', '1080.cv1', '1080.do1', '1080.dv1', '1080.fa1', '1080.fk1', '1080.fn1', '1080.ft1', '1080.ge1', '1080.hs1'], 'contains': ['4320.bh1', '6480.cx1', '6480.dd1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [482676004, 143975, 88695353644, 80787], 'label': '77760.bo.2160.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '2160.el1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.el1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055957
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dp1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.cc1', '720.dy1', '1080.y1', '1080.bt1', '1080.cw1', '1080.dj1', '1080.dw1', '1080.ey1', '1080.fe1', '1080.fl1', '1080.fv1', '1080.gd1', '1080.hk1'], 'contains': ['4320.bh1', '6480.cy1', '6480.de1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [482676004, 88695170185, 143975, 80787], 'label': '77760.bo.2160.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '2160.em1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.em1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055958
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['240.cd1', '720.dy1', '1080.z1', '1080.bs1', '1080.cw1', '1080.dl1', '1080.dx1', '1080.eu1', '1080.fb1', '1080.fi1', '1080.fw1', '1080.gb1', '1080.hn1'], 'contains': ['4320.bh1', '6480.cy1', '6480.df1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [482711044, 88695170185, 80880, 80787], 'label': '77760.bo.2160.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '2160.en1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.en1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246055959
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dp1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.j1', '720.dz1', '1080.x1', '1080.bu1', '1080.cx1', '1080.dq1', '1080.dw1', '1080.ez1', '1080.fh1', '1080.fk1', '1080.fq1', '1080.fw1', '1080.gj1'], 'contains': ['4320.bh1', '6480.cz1', '6480.dg1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [443120071204, 267845679213, 80880, 80787], 'label': '77760.bo.2160.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '2160.eo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.eo1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055960
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.k1', '720.dz1', '1080.ba1', '1080.br1', '1080.cx1', '1080.dr1', '1080.dx1', '1080.ex1', '1080.fa1', '1080.fj1', '1080.fp1', '1080.fv1', '1080.gq1'], 'contains': ['4320.bh1', '6480.cz1', '6480.dh1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [267845679358, 443120250115, 143975, 80787], 'label': '77760.bo.2160.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '2160.ep1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ep1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246055961
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '80.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.a1', '40.i1'], 'contains': ['160.c1', '160.f1', '160.h1', '240.bg1', '240.bl1', '240.bm1', '240.bn1', '240.bo1', '240.bp1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [180587456184, 93449001331, 143975, 83641651, 174400173363, 80880, 80787], 'label': '77760.bo.80.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '80.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.k1', 'subgroup_fusion': None, 'weyl_group': '1296.3538'}
  • id: 246055962
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.l1', '720.ea1', '1080.ba1', '1080.bu1', '1080.cu1', '1080.ds1', '1080.dv1', '1080.ew1', '1080.fb1', '1080.ff1', '1080.fl1', '1080.fu1', '1080.gx1'], 'contains': ['4320.bh1', '6480.da1', '6480.di1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [443120071204, 80880, 80787, 267845674052], 'label': '77760.bo.2160.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '2160.eq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.eq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246055963
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.dy1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.m1', '720.dv1', '1080.cy1', '1080.dy1', '1080.eb1', '1080.fs1', '1080.fx1'], 'contains': ['4320.bi1', '6480.cv1', '6480.dj1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [443120204759, 267845673867, 80787, 179159], 'label': '77760.bo.2160.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bi1', 'old_label': '2160.er1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.er1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056063
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2880.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['960.a1', '960.d1', '1440.bv1', '1440.df2'], 'contains': ['8640.d1', '8640.e1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 160, 'diagramx': None, 'generators': [280259705975, 193999420531, 80787], 'label': '77760.bo.2880.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '80.s1', 'old_label': '2880.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.i1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055964
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.dy1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.ce1', '720.dw1', '1080.cz1', '1080.dy1', '1080.ed1', '1080.fy1', '1080.ga1', '1080.gh1', '1080.ia1'], 'contains': ['4320.bi1', '6480.cw1', '6480.dk1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [482676004, 88695175204, 80787, 179159], 'label': '77760.bo.2160.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bi1', 'old_label': '2160.es1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.es1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055965
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.cf1', '720.dx1', '1080.cz1', '1080.dp1', '1080.dz1', '1080.fx1', '1080.ht1'], 'contains': ['4320.bi1', '6480.cx1', '6480.dl1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [482676004, 88695353644, 80787, 179159], 'label': '77760.bo.2160.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '2160.et1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.et1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055966
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.n1', '720.ea1', '1080.cy1', '1080.dt1', '1080.dz1', '1080.fy1', '1080.gy1'], 'contains': ['4320.bi1', '6480.da1', '6480.dm1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [443120204759, 80787, 267845674052, 179159], 'label': '77760.bo.2160.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '2160.eu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.eu1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055967
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.s1', '540.hj1', '720.eb1', '720.ek1', '1080.e1', '1080.bc1', '1080.da1'], 'contains': ['4320.bk1', '4320.bn1', '4320.br1', '6480.cj1', '6480.dn1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [442641300629, 998139594, 224515, 519200188], 'label': '77760.bo.2160.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '2160.ev1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ev1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055968
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.t1', '540.hk1', '720.eb1', '720.ec1', '720.el1', '1080.u1', '1080.bd1', '1080.cf1'], 'contains': ['4320.bj1', '4320.bp1', '4320.ca1', '6480.ck1', '6480.dn1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [174436496787, 368871234955, 375138172555, 80787], 'label': '77760.bo.2160.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '2160.ew1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ew1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055969
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.u1', '540.hl1', '720.ec1', '720.em1', '1080.g1', '1080.v1', '1080.da1'], 'contains': ['4320.bk1', '4320.bs1', '4320.cc1', '6480.cl1', '6480.dn1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [518918400, 997960349, 442641029309, 80880], 'label': '77760.bo.2160.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '2160.ex1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ex1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055970
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.v1', '540.hm1', '720.ed1', '720.ee1', '720.en1', '1080.bd1', '1080.cd1'], 'contains': ['4320.bj1', '4320.ce1', '4320.ch1', '6480.cm1', '6480.do1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [518964004, 997965813, 442641024598, 80787], 'label': '77760.bo.2160.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '2160.ey1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ey1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246055971
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.w1', '540.hn1', '720.ed1', '720.eo1', '1080.g1', '1080.bc1', '1080.cq1'], 'contains': ['4320.bk1', '4320.ck1', '4320.cu1', '6480.cn1', '6480.do1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [368871149398, 375138087093, 174436416243, 148], 'label': '77760.bo.2160.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '2160.ez1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ez1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055972
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '80.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.b1', '40.i1', '40.m1', '40.n1', '40.o1'], 'contains': ['160.c1', '160.d1', '240.bq1', '240.br1', '240.bs1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [180587277504, 93449001331, 143975, 83641651, 174400173363, 80880, 80787], 'label': '77760.bo.80.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '80.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.l1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246055973
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.x1', '540.ho1', '720.ee1', '720.ep1', '1080.cr1'], 'contains': ['4320.bl1', '4320.cm1', '4320.cv1', '6480.co1', '6480.do1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [442641386615, 997920598, 519280684, 179159], 'label': '77760.bo.2160.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ce1', 'old_label': '2160.fa1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.fa1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055974
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.ee1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.ef1', '720.eg1', '720.eh1', '1080.be1', '1080.bw1', '1080.db1', '1080.ea1', '1080.ee1', '1080.gj1', '1080.gm1', '1080.gq1', '1080.gv1', '1080.gx1', '1080.hc1', '1080.hk1', '1080.hn1', '1080.hs1', '1080.hz1'], 'contains': ['4320.bh1', '6480.dp1', '6480.dq1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [355499101444, 442681021680, 80880, 80787], 'label': '77760.bo.2160.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '2160.fb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.fb1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246055975
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.ef1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.eh1', '720.ei1', '720.ej1', '1080.dc1', '1080.eb1', '1080.ef1', '1080.gy1', '1080.hd1', '1080.ht1', '1080.ia1'], 'contains': ['4320.bi1', '6480.dp1', '6480.dr1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [442680940800, 355499245412, 80787, 179159], 'label': '77760.bo.2160.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.k1', 'old_label': '2160.fc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.fc1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055976
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.cj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.o1', '720.ef1', '720.ei1', '1080.bf1', '1080.cg1', '1080.eg1', '1080.en1', '1080.gn1', '1080.gr1', '1080.gw1', '1080.gz1', '1080.ho1', '1080.hu1', '1080.if1'], 'contains': ['6480.dp1', '6480.ds1', '6480.dt1', '8640.c1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [274467962404, 194518195200, 268244605587, 80787], 'label': '77760.bo.2160.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '2160.fd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.fd1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246055977
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.ef1', '720.eg1', '720.ej1', '1080.bg1', '1080.eh1', '1080.go1', '1080.gs1', '1080.ha1', '1080.hp1', '1080.hv1'], 'contains': ['6480.dp1', '6480.du1', '8640.d1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [442680940800, 355499020800, 355419232563, 80787], 'label': '77760.bo.2160.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1', 'old_label': '2160.fe1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.fe1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246055978
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.eg1', '720.ei1', '720.ej1', '1080.ei1', '1080.hb1', '1080.hw1'], 'contains': ['6480.dp1', '6480.dv1', '8640.e1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [274467962404, 194518374451, 268244605587, 80787], 'label': '77760.bo.2160.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.bb1', 'old_label': '2160.ff1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ff1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 246055979
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['432.p1', '720.ef1', '1080.h1', '1080.bh1', '1080.dd1', '1080.ej1', '1080.eo1', '1080.gi1', '1080.gk1', '1080.gp1', '1080.gt1', '1080.he1', '1080.hi1', '1080.hl1', '1080.hq1', '1080.hx1', '1080.ig1'], 'contains': ['6480.dq1', '6480.ds1', '6480.du1', '8640.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [274467916800, 268244524800, 143975, 194518339175], 'label': '77760.bo.2160.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '2160.fg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.fg1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246055980
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.ef1', '1080.de1', '1080.ek1', '1080.gl1', '1080.gu1', '1080.hf1', '1080.hm1', '1080.hr1'], 'contains': ['6480.dq1', '6480.dt1', '6480.du1', '8640.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [355499101444, 45363, 355419187348, 442680986163], 'label': '77760.bo.2160.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.z1', 'old_label': '2160.fh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.fh1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246055981
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.q1', '720.ei1', '1080.df1', '1080.el1', '1080.ep1', '1080.hg1', '1080.hj1', '1080.hy1', '1080.ih1'], 'contains': ['6480.dr1', '6480.ds1', '6480.dv1', '8640.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [274467916800, 194518374359, 268244524800, 179159], 'label': '77760.bo.2160.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '2160.fi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.fi1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246055982
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.ei1', '1080.dg1', '1080.em1', '1080.hh1'], 'contains': ['6480.dr1', '6480.dt1', '6480.dv1', '8640.i1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [274467916800, 268244524800, 194518419812, 179159], 'label': '77760.bo.2160.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.cd1', 'old_label': '2160.fj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.fj1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 246055983
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '80.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.b1', '40.c1', '40.j1', '40.m1', '40.p1', '40.q1', '40.r1'], 'contains': ['160.d1', '160.e1', '240.bt1', '240.bw1', '240.bx1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [180587277504, 93449001331, 83467916, 143975, 174400173363, 80880, 80787], 'label': '77760.bo.80.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '80.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.m1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246055984
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.w1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.ek1', '720.el1', '720.em1', '1080.f1', '1080.i1', '1080.ch1', '1080.eq1', '1080.ib1', '1080.ic1', '1080.id1'], 'contains': ['4320.bm1', '4320.bx1', '6480.dn1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [456053154955, 174400128000, 180587232000, 93448857600], 'label': '77760.bo.2160.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '2160.fk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.fk1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246055985
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.en1', '720.eo1', '720.ep1', '1080.i1', '1080.ce1', '1080.er1', '1080.ib1', '1080.ie1'], 'contains': ['4320.bm1', '4320.cr1', '6480.do1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [456053069398, 174400128000, 180587232000, 93448857600], 'label': '77760.bo.2160.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '2160.fl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.fl1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246055986
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1', '720.eq1', '720.et1', '720.ex1', '1080.j1', '1080.ci1', '1080.es1', '1080.ic1', '1080.ie1'], 'contains': ['4320.bm1', '19440.r1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 10, 'diagramx': None, 'generators': [280259481600, 88695129600, 482630400, 193999276800], 'label': '77760.bo.2160.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '2160.fm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.fm1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246055987
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.er1', '720.eu1', '720.ey1', '1080.k1', '1080.ci1', '1080.er1', '1080.id1'], 'contains': ['4320.bm1', '19440.s1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [280259481600, 482630400, 88695272904, 193999276800], 'label': '77760.bo.2160.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '2160.fn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.fn1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246055988
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.es1', '720.ev1', '720.ew1', '1080.j1', '1080.k1', '1080.cj1', '1080.eq1', '1080.ib1'], 'contains': ['4320.bm1', '19440.t1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [280259481600, 482630400, 193999276800, 88695348625], 'label': '77760.bo.2160.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '2160.fo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.fo1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246055989
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gm1', '720.ez1', '720.fa1', '720.fb1', '1080.a1', '1080.bc1', '1080.cp1'], 'contains': ['4320.bn1', '4320.cu1', '4320.dc1', '6480.dw1', '6480.dx1', '6480.dy1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [997920598, 518918400, 442641110396, 148], 'label': '77760.bo.2160.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '2160.fp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.fp1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055990
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.ez1', '720.fc1', '720.fh1', '1080.o1', '1080.bq1', '1080.ck1', '1080.dh2', '1080.dh3', '1080.et1', '1080.et2'], 'contains': ['4320.bo1', '4320.cf1', '4320.cz1', '6480.dw1', '6480.dz1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [87182277597, 143975, 375138270474, 80787], 'label': '77760.bo.2160.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bj1', 'old_label': '2160.fq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.fq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055991
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.fq2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.fh2', '1080.o2', '1080.bq2', '1080.ck2', '1080.dh1', '1080.dh4', '1080.et1', '1080.et2'], 'contains': ['4320.bo1', '4320.cf1', '4320.cz1', '6480.dw2', '6480.dz2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [442641386852, 448908283441, 143975, 80787], 'label': '77760.bo.2160.fq2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '2160.fq2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.fq2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055992
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gr1', '720.ez1', '720.fe1', '720.ff1', '1080.p1', '1080.bd1', '1080.ca1'], 'contains': ['4320.bp1', '4320.ch1', '4320.da1', '6480.dx1', '6480.dz1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [174436496787, 368871230130, 375138172555, 80787], 'label': '77760.bo.2160.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '2160.fr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.fr1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055993
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gs1', '720.ez1', '720.fd1', '720.fg1', '1080.q1'], 'contains': ['4320.bq1', '4320.ci1', '4320.db1', '6480.dy1', '6480.dz1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [442641110155, 997965813, 518963763, 80787], 'label': '77760.bo.2160.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.q1', 'old_label': '2160.fs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.fs1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055994
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '80.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.c1', '40.i1', '40.n1', '40.p1', '40.s1'], 'contains': ['160.d1', '160.f1', '240.bu1', '240.by1', '240.bz1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [180587277504, 93449001331, 143975, 174400173363, 456053150130, 80880, 80787], 'label': '77760.bo.80.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '80.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.n1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246055995
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.go1', '720.fb1', '720.fc1', '1080.b1', '1080.bc1', '1080.cl1'], 'contains': ['4320.br1', '4320.ck1', '4320.dc1', '6480.dw1', '6480.ea1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [518918400, 997961035, 148, 442641024450], 'label': '77760.bo.2160.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '2160.ft1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ft1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055996
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gp1', '720.fa1', '720.fc1', '1080.cm1'], 'contains': ['4320.bt1', '4320.cl1', '4320.dd1', '6480.dw1', '6480.eb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [518964004, 997961035, 148, 442641024450], 'label': '77760.bo.2160.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.cm1', 'old_label': '2160.fu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.fu1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055997
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.fa1', '720.fe1', '720.fi1', '1080.cb1'], 'contains': ['4320.bu1', '4320.co1', '4320.de1', '6480.dx1', '6480.eb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [83548555, 174400208787, 93448938387, 180587272349], 'label': '77760.bo.2160.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.cb1', 'old_label': '2160.fv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.fv1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055998
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.fb1', '720.fd1', '1080.c1'], 'contains': ['4320.bw1', '4320.cp1', '4320.df1', '6480.dy1', '6480.ea1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [93449082115, 83462998, 180587415845, 174400352515], 'label': '77760.bo.2160.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.c1', 'old_label': '2160.fw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.fw1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246055999
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.fb1', '720.fe1', '720.fj1', '1080.d1', '1080.i1', '1080.cc1'], 'contains': ['4320.bx1', '4320.cr1', '4320.dg1', '6480.dx1', '6480.ea1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [456053069398, 174400128000, 180587272349, 93448857600], 'label': '77760.bo.2160.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.j1', 'old_label': '2160.fx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.fx1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056000
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.fa1', '720.fd1'], 'contains': ['4320.by1', '4320.cs1', '4320.dh1', '6480.dy1', '6480.eb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 8640, 'diagramx': None, 'generators': [83462998, 174400307012, 180587415845, 93449001575], 'label': '77760.bo.2160.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2160.fy1', 'old_label': '2160.fy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.fy1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056001
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gt1', '720.ff1', '720.fi1', '720.fj1', '1080.g1', '1080.n1', '1080.cp1'], 'contains': ['4320.bs1', '4320.cu1', '4320.cx1', '6480.dx1', '6480.ec1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [997920598, 224515, 442641301050, 519200188], 'label': '77760.bo.2160.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '2160.fz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.fz1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056002
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gy1', '720.fk1', '720.fl1', '1080.b1', '1080.n1', '1080.da1'], 'contains': ['4320.br1', '4320.bs1', '4320.dn1', '6480.ed1', '6480.ee1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [998139594, 224515, 442641301050, 519200188], 'label': '77760.bo.2160.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '2160.ga1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ga1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056005
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '80.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '40.d1', '40.k1', '40.o1', '40.q1', '40.s1'], 'contains': ['160.d1', '240.ca1', '240.ce1', '720.dw1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 10, 'diagramx': None, 'generators': [143975, 80787, 482711044, 280259527104, 193999455812, 88695175204, 80880], 'label': '77760.bo.80.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '80.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.o1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246056006
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gu1', '720.fc1', '720.fd1', '720.fe1', '720.fr1', '1080.t1', '1080.bd1', '1080.bz1'], 'contains': ['4320.ca1', '4320.ce1', '4320.da1', '6480.dz1', '6480.ea1', '6480.eb1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [518964004, 997925759, 80787, 442641024450], 'label': '77760.bo.2160.gd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '2160.gd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.gd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056007
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.ff1', '720.fg1', '720.fh1', '720.fr1', '1080.w1', '1080.bo1', '1080.ck1', '1080.dh1', '1080.dh3', '1080.fd1', '1080.fd2'], 'contains': ['4320.bz1', '4320.cf1', '4320.cw1', '6480.dz1', '6480.ec1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [87182277125, 143975, 375138172555, 80787], 'label': '77760.bo.2160.ge1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bj1', 'old_label': '2160.ge1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ge1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056008
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.ge2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.fh2', '1080.w2', '1080.bo2', '1080.ck2', '1080.dh2', '1080.dh4', '1080.fd1', '1080.fd2'], 'contains': ['4320.bz1', '4320.cf1', '4320.cw1', '6480.dz2', '6480.ec2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [448908278999, 442641109705, 80880, 80787], 'label': '77760.bo.2160.ge2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '2160.ge2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ge2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056009
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gw1', '720.fj1', '720.fr1', '1080.g1', '1080.s1', '1080.cl1'], 'contains': ['4320.cc1', '4320.ck1', '4320.cx1', '6480.ea1', '6480.ec1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [997925759, 179012, 519235320, 442641341252], 'label': '77760.bo.2160.gf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '2160.gf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.gf1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056010
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gx1', '720.fi1', '720.fr1', '1080.cm1'], 'contains': ['4320.cd1', '4320.cl1', '4320.cy1', '6480.eb1', '6480.ec1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [997925759, 519280587, 179012, 442641341252], 'label': '77760.bo.2160.gg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.cm1', 'old_label': '2160.gg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.gg1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056011
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.gz1', '720.fk1', '720.fs1', '1080.a1', '1080.s1', '1080.da1'], 'contains': ['4320.bn1', '4320.cc1', '4320.dn1', '6480.ed1', '6480.ee1', '6480.ef1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [518918400, 45363, 442641300958, 997960349], 'label': '77760.bo.2160.gh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '2160.gh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.gh1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056012
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.fl1', '720.fm1', '720.fn1', '720.fs1', '1080.o1', '1080.bo1', '1080.cs1', '1080.dh3', '1080.dh4', '1080.fm1', '1080.fm2'], 'contains': ['4320.bo1', '4320.bz1', '4320.di1', '6480.ed1', '6480.eg1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [87182202116, 143975, 375138270474, 80787], 'label': '77760.bo.2160.gi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bj1', 'old_label': '2160.gi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.gi1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056013
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.gi2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.fn2', '1080.o2', '1080.bo2', '1080.cs2', '1080.dh1', '1080.dh2', '1080.fm1', '1080.fm2'], 'contains': ['4320.bo1', '4320.bz1', '4320.di1', '6480.ed2', '6480.eg2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [442641109705, 80880, 80787, 448908283914], 'label': '77760.bo.2160.gi2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '2160.gi2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.gi2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056014
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.hb1', '720.fl1', '720.fo1', '720.fp1', '720.fs1', '1080.p1', '1080.t1', '1080.cf1'], 'contains': ['4320.bp1', '4320.ca1', '4320.dk1', '6480.ee1', '6480.eg1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [518964004, 442641301050, 997960349, 80787], 'label': '77760.bo.2160.gj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '2160.gj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.gj1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056015
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.hc1', '720.fm1', '720.fo1', '720.fq1', '720.fs1', '1080.q1'], 'contains': ['4320.bq1', '4320.cb1', '4320.dl1', '6480.ef1', '6480.eg1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [518963763, 442641301050, 997960349, 80787], 'label': '77760.bo.2160.gk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.q1', 'old_label': '2160.gk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.gk1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056016
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '80.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.e1', '40.k1', '40.n1', '40.r1'], 'contains': ['160.d1', '240.cb1', '240.cf1', '720.dx1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 10, 'diagramx': None, 'generators': [482711044, 143975, 88695353644, 193999455812, 280259527104, 80880, 80787], 'label': '77760.bo.80.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '80.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.p1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246056017
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2160.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.ft1', '1080.bb1', '1080.bv1', '1080.ct1', '1080.dh1', '1080.dh2', '1080.dh3', '1080.dh4'], 'contains': ['4320.cw1', '4320.cz1', '4320.di1', '6480.eh1', '6480.ei1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [143975, 268244748747, 274468002505, 80787], 'label': '77760.bo.2160.gl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bj1', 'old_label': '2160.gl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.gl1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056018
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2430.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['810.a1', '810.o1', '810.p1', '1215.a1'], 'contains': ['4860.a1', '4860.e1', '4860.k1', '4860.l1', '4860.m1', '4860.bm1', '4860.bp1', '4860.br1', '4860.bz1', '4860.ca1', '4860.cd1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [357597, 19678982400, 448908001949, 462320363997, 461841045149], 'label': '77760.bo.2430.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '2430.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2430.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056019
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2430.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['810.b1', '810.g1', '810.q1', '810.r1', '1215.a1'], 'contains': ['4860.d1', '4860.e2', '4860.f1', '4860.i1', '4860.k1', '4860.o1', '4860.p1', '4860.bm2', '4860.bn1', '4860.bs1', '4860.bt1', '4860.ca1', '4860.cb1', '4860.ce1', '4860.cg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [183845, 19678982400, 448908001949, 461841045149, 462320046749], 'label': '77760.bo.2430.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '2430.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2430.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056020
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2430.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['810.c1', '810.s1', '810.t1', '1215.a1'], 'contains': ['4860.c1', '4860.e2', '4860.g1', '4860.j1', '4860.m1', '4860.bm2', '4860.bo1', '4860.bu1', '4860.bv1', '4860.cc1', '4860.cd1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [19678982400, 462320011709, 448908284158, 461841010109, 322558], 'label': '77760.bo.2430.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '2430.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2430.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056021
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2430.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['810.d1', '810.e1', '810.f1', '810.u1', '810.v1', '1215.a1'], 'contains': ['4860.b1', '4860.c1', '4860.d1', '4860.e1', '4860.h1', '4860.n1', '4860.p1', '4860.bm1', '4860.bn1', '4860.bo1', '4860.bq1', '4860.bw1', '4860.bx1', '4860.cf1', '4860.cg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [183845, 462320190245, 461841188645, 19678982400, 448908001949], 'label': '77760.bo.2430.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '2430.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2430.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056022
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2430.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.ck2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['810.h1', '810.i1', '810.w1', '810.x1', '1215.a1'], 'contains': ['4860.a1', '4860.f1', '4860.g1', '4860.h1', '4860.q1', '4860.bp1', '4860.bs1', '4860.bu1', '4860.bw1', '4860.by1', '4860.ch1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [40349, 19678982400, 448908001949, 461841045149, 462320046749], 'label': '77760.bo.2430.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '2430.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2430.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056023
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2430.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['810.j1', '810.k1', '810.y1', '810.z1', '1215.a1'], 'contains': ['4860.j1', '4860.l1', '4860.n1', '4860.o1', '4860.q1', '4860.bz1', '4860.cc1', '4860.ce1', '4860.cf1', '4860.ch1', '4860.ci1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [183845, 461841188645, 19678982400, 448908001949, 462320046749], 'label': '77760.bo.2430.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '2430.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2430.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056024
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2430.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['810.ba1', '810.bf1', '1215.a1'], 'contains': ['4860.a1', '4860.b1', '4860.i1', '4860.j1', '4860.r2', '4860.s1', '4860.t1', '4860.y1', '4860.z1', '4860.be1', '4860.bf1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1215, 'diagramx': None, 'generators': [462320092205, 7185207845, 19678982400, 85805, 143304], 'label': '77760.bo.2430.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '2430.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2430.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056025
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2430.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['810.m1', '810.bb1', '810.bg1', '1215.a1'], 'contains': ['4860.c1', '4860.f1', '4860.k1', '4860.n1', '4860.r1', '4860.s1', '4860.u1', '4860.x1', '4860.ba1', '4860.bd1', '4860.bi1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [443120025600, 442641024000, 180667203842, 5066, 143304], 'label': '77760.bo.2430.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '2430.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2430.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056026
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2430.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['270.e1', '810.bc1', '810.bh1', '1215.a1'], 'contains': ['4860.d1', '4860.g1', '4860.l1', '4860.r1', '4860.t1', '4860.w1', '4860.bb1', '4860.bg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1215, 'diagramx': None, 'generators': [87261753600, 83462998, 598, 456053154955, 85946], 'label': '77760.bo.2430.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '2430.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2430.i1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056027
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '80.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.d1', '40.e1', '40.l1', '40.m1', '40.p1'], 'contains': ['160.d1', '240.cc1', '240.cd1', '720.dy1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [482711044, 143975, 193999455812, 280259527104, 80880, 80787, 88695348625], 'label': '77760.bo.80.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '80.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.q1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246056028
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2430.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['810.l1', '810.bd1', '810.bi1', '1215.a1'], 'contains': ['4860.e1', '4860.e2', '4860.h1', '4860.o1', '4860.r1', '4860.r2', '4860.u1', '4860.v1', '4860.v2', '4860.bc1', '4860.bj1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [362615, 19678982400, 40585, 448908284158, 462320046985], 'label': '77760.bo.2430.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '2430.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2430.j1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056029
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2430.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['810.n1', '810.be1', '810.bj1', '1215.a1'], 'contains': ['4860.m1', '4860.p1', '4860.q1', '4860.t1', '4860.u1', '4860.bh1', '4860.bk1', '4860.bl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1215, 'diagramx': None, 'generators': [87182277597, 355938191305, 317252, 374659442397, 85705], 'label': '77760.bo.2430.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '2430.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2430.k1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056030
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2430.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['810.bk1', '810.bv1', '1215.a1'], 'contains': ['4860.v1', '4860.y1', '4860.bd1', '4860.bg1', '4860.bh1', '4860.bp1', '4860.bq1', '4860.cb1', '4860.cc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1215, 'diagramx': None, 'generators': [19678982400, 448908284158, 461841010109, 462320006400, 317252], 'label': '77760.bo.2430.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '2430.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2430.l1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056031
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2430.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['810.bl1', '810.bq1', '810.bw1', '1215.a1'], 'contains': ['4860.v2', '4860.w1', '4860.ba1', '4860.bd1', '4860.be1', '4860.bj1', '4860.bk1', '4860.bo1', '4860.bs1', '4860.ca1', '4860.cf1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [461841004800, 281971, 19678982400, 448908243571, 462320046749], 'label': '77760.bo.2430.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '2430.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2430.m1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056032
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2430.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['810.bm1', '810.bx1', '1215.a1'], 'contains': ['4860.v2', '4860.x1', '4860.bb1', '4860.bf1', '4860.bh1', '4860.bn1', '4860.bu1', '4860.bz1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1215, 'diagramx': None, 'generators': [461841009961, 281971, 462320011561, 19678982400, 448908243571], 'label': '77760.bo.2430.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '2430.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2430.n1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056033
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2430.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['810.bn1', '810.bo1', '810.bp1', '810.by1', '1215.a1'], 'contains': ['4860.v1', '4860.w1', '4860.x1', '4860.z1', '4860.bc1', '4860.bi1', '4860.bk1', '4860.bm1', '4860.bm2', '4860.bw1', '4860.ce1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [461841009961, 281971, 19678982400, 448908243571, 462320006400], 'label': '77760.bo.2430.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '2430.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2430.o1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056034
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2430.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.co2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['810.br1', '810.bs1', '810.bz1', '810.ca1', '1215.a1'], 'contains': ['4860.y1', '4860.ba1', '4860.bb1', '4860.bc1', '4860.bl1', '4860.br1', '4860.bt1', '4860.bv1', '4860.bx1', '4860.by1', '4860.ci1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [461841004800, 281971, 19678982400, 448908243571, 462320006400], 'label': '77760.bo.2430.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '2430.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2430.p1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056035
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2430.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['810.bt1', '810.bu1', '810.cb1', '1215.a1'], 'contains': ['4860.bf1', '4860.bg1', '4860.bi1', '4860.bj1', '4860.bl1', '4860.cd1', '4860.cg1', '4860.ch1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1215, 'diagramx': None, 'generators': [461841004800, 362615, 19678982400, 448908284158, 462320046985], 'label': '77760.bo.2430.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '2430.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2430.q1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056036
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2592.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.a1', '1296.a1', '1296.b1', '1296.g1'], 'contains': ['5184.b1', '7776.a1', '12960.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [18764743922, 138242, 80880], 'label': '77760.bo.2592.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d1', 'old_label': '2592.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 246056037
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2592.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.a1', '864.b1', '1296.c1', '1296.f1', '1296.h1'], 'contains': ['5184.a1', '7776.a1', '12960.d1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [5309, 80787, 18764565242], 'label': '77760.bo.2592.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '2592.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.b1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 246056038
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '80.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.a1', '40.c1', '40.h1'], 'contains': ['160.e1', '160.f1', '160.g1', '240.cg1', '240.ch1', '240.ci1', '240.cj1', '240.ck1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 80, 'diagramx': None, 'generators': [93449001331, 143975, 174400173363, 456053150130, 180587272349, 80880, 80787], 'label': '77760.bo.80.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '80.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.r1', 'subgroup_fusion': None, 'weyl_group': '3888.ik'}
  • id: 246056039
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2592.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.b1', '1296.d1', '1296.e1', '1296.g1'], 'contains': ['5184.b1', '7776.a1', '12960.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [138242, 143975, 18764663042], 'label': '77760.bo.2592.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d1', 'old_label': '2592.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.c1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 246056040
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2592.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.c1', '864.d1', '1296.h1', '1296.i1', '1296.j1'], 'contains': ['5184.a1', '7776.b1', '12960.f1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [18764748747, 178680, 80787], 'label': '77760.bo.2592.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.e1', 'old_label': '2592.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.d1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 246056041
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2592.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.c1', '1296.g1', '1296.k1', '1296.m1'], 'contains': ['5184.b1', '7776.b1', '12960.i1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [179012, 178680, 18764703480], 'label': '77760.bo.2592.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '2592.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.e1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 246056042
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2592.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.d1', '1296.l1'], 'contains': ['5184.c1', '7776.b1', '12960.j1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [178680, 18764703480, 179159], 'label': '77760.bo.2592.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.m1', 'old_label': '2592.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.f1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 246056043
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2592.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.o1', '864.e1', '864.f1', '1296.c1', '1296.i1', '1296.n1', '1296.o1', '1296.p1'], 'contains': ['5184.a1', '7776.c1', '12960.s1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1037836800, 18764605587, 80787], 'label': '77760.bo.2592.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '2592.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.g1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 246056044
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2592.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.p1', '864.e1', '1296.a1', '1296.d1', '1296.k1', '1296.q1', '1296.r1', '1296.s1', '1296.t1'], 'contains': ['5184.b1', '7776.c1', '12960.t1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1037836800, 18764605680, 80880], 'label': '77760.bo.2592.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '2592.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.h1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 246056045
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2592.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.q1', '864.f1', '1296.l1', '1296.u1', '1296.v1'], 'contains': ['5184.c1', '7776.c1', '12960.u1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1037836800, 18764524800, 179159], 'label': '77760.bo.2592.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.m1', 'old_label': '2592.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.i1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 246056046
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2592.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.g1', '1296.a1', '1296.e1', '1296.m1'], 'contains': ['5184.b1', '7776.d1', '12960.bm1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1038020645, 18764605680, 80880], 'label': '77760.bo.2592.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d1', 'old_label': '2592.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.j1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 246056047
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2592.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.g1', '864.h1', '1296.c1', '1296.f1', '1296.j1'], 'contains': ['5184.a1', '7776.d1', '12960.bn1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [18764605587, 80787, 1037922605], 'label': '77760.bo.2592.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '2592.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.k1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246056048
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2592.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.h1', '1296.b1', '1296.d1', '1296.m1'], 'contains': ['5184.b1', '7776.d1', '12960.bo1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [45363, 18764570163, 1037922605], 'label': '77760.bo.2592.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d1', 'old_label': '2592.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.l1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246056049
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '80.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.a1', '40.j1'], 'contains': ['160.e1', '160.h1', '240.cl1', '240.cm1', '240.cn1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [180587456184, 456053207518, 93449001331, 143975, 174400173363, 80880, 80787], 'label': '77760.bo.80.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '80.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.s1', 'subgroup_fusion': None, 'weyl_group': '3888.ik'}
  • id: 246056050
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2592.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.i1', '864.j1', '1296.f1', '1296.i1'], 'contains': ['5184.a1', '7776.e1', '12960.bs1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1037980104, 18764605587, 80787], 'label': '77760.bo.2592.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.e1', 'old_label': '2592.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.m1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 246056051
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2592.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.i1', '1296.b1', '1296.e1', '1296.k1'], 'contains': ['5184.b1', '7776.e1', '12960.bt1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1037980104, 18764605680, 80880], 'label': '77760.bo.2592.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '2592.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.n1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246056052
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2592.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.j1', '1296.l1'], 'contains': ['5184.c1', '7776.e1', '12960.bu1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1037980104, 143731, 18764524800], 'label': '77760.bo.2592.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.m1', 'old_label': '2592.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.o1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246056053
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2880.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': ['27.a1'], 'conjugacy_class_count': 1, 'contained_in': ['576.a1', '960.c1', '1440.a1', '1440.b1', '1440.s1', '1440.be1', '1440.br1', '1440.cg1', '1440.cp1', '1440.cz1'], 'contains': ['8640.a1', '8640.b1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [143975, 80880, 80787], 'label': '77760.bo.2880.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2880.a1', 'normal_contained_in': ['8.a1', '1440.a1', '1440.b1'], 'normal_contains': ['8640.a1'], 'normalizer': '1.a1', 'old_label': '2880.a1', 'projective_image': '77760.bo', 'quotient_action_image': '4.2', 'quotient_action_kernel': '720.763', 'quotient_action_kernel_order': 720, 'quotient_fusion': None, 'short_label': '2880.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056054
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2880.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '480.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.ef1', '960.a1', '960.b1', '960.c1', '1440.d1', '1440.h1', '1440.k1', '1440.q1', '1440.v1', '1440.bf1', '1440.bk1', '1440.bn1', '1440.bo1', '1440.by1', '1440.bz1', '1440.ce1', '1440.cn1', '1440.cs1', '1440.cx1'], 'contains': ['8640.a1', '8640.c1', '8640.d1', '8640.f1', '8640.g1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 80, 'diagramx': None, 'generators': [355419232563, 80880, 80787], 'label': '77760.bo.2880.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '2880.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056055
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2880.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.z1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['720.eg1', '960.a1', '960.c1', '1440.i1', '1440.r1', '1440.bp1', '1440.bq1', '1440.cf1', '1440.co1', '1440.cy1'], 'contains': ['8640.a1', '8640.d1', '8640.e1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 160, 'diagramx': None, 'generators': [194518374451, 80880, 80787], 'label': '77760.bo.2880.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.a1', 'old_label': '2880.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.c1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056056
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2880.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '480.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.ei1', '960.c1', '960.d1', '960.e1', '1440.l1', '1440.t1', '1440.w1', '1440.bg1', '1440.ca1', '1440.ch1', '1440.da1'], 'contains': ['8640.b1', '8640.c1', '8640.e1', '8640.h1', '8640.i1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 80, 'diagramx': None, 'generators': [80787, 355419504267, 179159], 'label': '77760.bo.2880.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.i1', 'old_label': '2880.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056057
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2880.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.ej1', '960.c1', '960.d1', '1440.u1', '1440.ci1', '1440.db1'], 'contains': ['8640.b1', '8640.d1', '8640.e1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 160, 'diagramx': None, 'generators': [194518374451, 80787, 179159], 'label': '77760.bo.2880.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '80.k1', 'old_label': '2880.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.e1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 246056058
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2880.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '960.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['960.a1', '960.b1', '960.d1', '1440.e1', '1440.x1', '1440.bs1', '1440.bt1', '1440.cb1', '1440.ct1', '1440.dc1'], 'contains': ['8640.c1', '8640.d1', '8640.k1', '8640.n1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 160, 'diagramx': None, 'generators': [193999276948, 280259527104, 80787], 'label': '77760.bo.2880.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.a1', 'old_label': '2880.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.f1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056059
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2880.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '960.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['960.a1', '960.d1', '960.e1', '1440.y1', '1440.cc1', '1440.dd1'], 'contains': ['8640.c1', '8640.e1', '8640.l1', '8640.o1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 160, 'diagramx': None, 'generators': [280259481600, 193999420531, 80787], 'label': '77760.bo.2880.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '80.k1', 'old_label': '2880.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.g1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056060
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.e1', '3.a1'], 'contains': ['12.c1', '12.h1', '12.m1', '18.k1', '18.n1', '36.n1', '60.t1', '90.bd1'], 'core': '12.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [93924311494, 80880, 80787, 462320046985, 693], 'label': '77760.bo.6.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1', 'subgroup_fusion': None, 'weyl_group': '25920.w'}
  • id: 246056061
    {'ambient': '77760.bo', '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': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['30.a1', '45.a1'], 'contains': ['180.d1', '180.k1', '180.l1', '180.dt1', '180.du1', '180.el1', '180.ev1', '270.a1', '270.j1', '270.k1', '270.l1', '360.f1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841090505, 143975, 80787, 462320328485, 448908284158, 19679028004, 262496684612, 5309], 'label': '77760.bo.90.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '90.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.a1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246056062
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2880.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '160.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['960.b1', '960.e1', '1440.f1', '1440.j1', '1440.z1', '1440.bh1', '1440.bu1', '1440.cd1', '1440.cu1', '1440.de1'], 'contains': ['8640.c1', '8640.j1', '8640.m1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 10, 'diagramx': None, 'generators': [280259481600, 80787, 193999357587], 'label': '77760.bo.2880.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '2880.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.h1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 246056065
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2880.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '960.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['960.b1', '1440.m1', '1440.ba1', '1440.bl1', '1440.bw1', '1440.cj1', '1440.cq1', '1440.cv1'], 'contains': ['8640.f1', '8640.g1', '8640.j1', '8640.k1', '8640.n1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [280259481600, 143975, 193999455812], 'label': '77760.bo.2880.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.v1', 'old_label': '2880.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.j1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246056066
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2880.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '480.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['960.b1', '1440.c1', '1440.g1', '1440.n1', '1440.bb1', '1440.bi1', '1440.bm1', '1440.bx1', '1440.ck1', '1440.cr1', '1440.cw1', '1440.dg1'], 'contains': ['8640.f1', '8640.k1', '8640.m1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [193999276800, 280259527104, 80880], 'label': '77760.bo.2880.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '2880.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.k1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 246056067
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2880.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '960.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['960.e1', '1440.o1', '1440.bc1', '1440.cl1'], 'contains': ['8640.h1', '8640.i1', '8640.j1', '8640.l1', '8640.o1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [280259481600, 193999420531, 179159], 'label': '77760.bo.2880.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.u1', 'old_label': '2880.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.l1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056068
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2880.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '960.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['960.e1', '1440.p1', '1440.bd1', '1440.bj1', '1440.cm1', '1440.dh1'], 'contains': ['8640.h1', '8640.l1', '8640.m1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [280259481600, 193999455959, 179159], 'label': '77760.bo.2880.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.s1', 'old_label': '2880.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.m1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 246056069
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.a1', '1080.b1', '1080.o1', '1620.e1', '1620.e2', '1620.ck1'], 'contains': ['6480.a1', '6480.h1', '6480.k1', '6480.bt1', '6480.by1', '6480.dw1', '6480.ed1', '9720.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [442641386187, 143975, 443120026293, 85805], 'label': '77760.bo.3240.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bd1', 'old_label': '3240.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056070
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.a2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.o2', '1620.e1', '1620.e2', '1620.ck2'], 'contains': ['6480.a1', '6480.h1', '6480.k1', '6480.bt2', '6480.by2', '6480.dw2', '6480.ed2', '9720.a2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [442641305971, 448908283441, 224515, 85946], 'label': '77760.bo.3240.a2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.a2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056071
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['810.e1', '1080.a1', '1080.d1', '1080.n1', '1080.p1', '1620.ba1'], 'contains': ['6480.b1', '6480.i1', '6480.l1', '6480.bu1', '6480.ca1', '6480.dx1', '6480.ee1', '9720.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 6480, 'diagramx': None, 'generators': [997920598, 40349, 518918400, 442641024000], 'label': '77760.bo.3240.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1620.ba1', 'old_label': '3240.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056072
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['30.b1', '45.a1'], 'contains': ['180.e1', '180.j1', '180.l1', '180.ea1', '180.eb1', '180.em1', '180.es1', '270.b1', '270.g1', '270.n1', '360.h1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [80787, 461841281758, 262496586387, 19678982548, 448908283914, 277050, 80880, 462320046985], 'label': '77760.bo.90.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '90.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.b1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246056073
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['810.f1', '1080.a1', '1080.c1', '1080.q1'], 'contains': ['6480.c1', '6480.j1', '6480.m1', '6480.bw1', '6480.cb1', '6480.dy1', '6480.ef1', '9720.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 12960, 'diagramx': None, 'generators': [997920598, 40349, 442641024000, 519200188], 'label': '77760.bo.3240.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3240.c1', 'old_label': '3240.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056074
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.e1', '1080.r1', '1620.c1', '1620.d1', '1620.e2', '1620.f1', '1620.g1', '1620.h1', '1620.ck1'], 'contains': ['6480.a1', '6480.e1', '6480.br1', '6480.ce1', '6480.cj1', '9720.b1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [183845, 442641104880, 443120025600, 80880], 'label': '77760.bo.3240.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056075
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.d2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.r2', '1620.a1', '1620.b1', '1620.e1', '1620.h1', '1620.ck2'], 'contains': ['6480.a1', '6480.e1', '6480.br2', '6480.ce2', '6480.cj2', '9720.b2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [448908283441, 224515, 85946, 442641305788], 'label': '77760.bo.3240.d2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.d2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.d2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056076
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['810.g1', '1080.b1', '1080.c1', '1080.d1', '1080.s1', '1080.t1', '1620.ba1'], 'contains': ['6480.d1', '6480.g1', '6480.l1', '6480.cg1', '6480.ch1', '6480.ea1', '6480.ee1', '9720.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 6480, 'diagramx': None, 'generators': [86155, 174436502155, 368871234955, 375138172205], 'label': '77760.bo.3240.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1620.ba1', 'old_label': '3240.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056077
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['324.a1', '810.i1', '1080.e1', '1080.f1', '1080.u1', '1080.v1', '1620.ba1'], 'contains': ['6480.b1', '6480.d1', '6480.f1', '6480.bu1', '6480.cg1', '6480.ci1', '6480.dn1', '9720.b1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [375138091561, 5161, 174436421161, 368871153961], 'label': '77760.bo.3240.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '3240.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056078
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.g1', '1080.w1', '1620.d1', '1620.e1', '1620.n1', '1620.o1', '1620.r1', '1620.u1', '1620.ck1'], 'contains': ['6480.e1', '6480.h1', '6480.cl1', '6480.cn1', '6480.ec1', '9720.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [87182196721, 143975, 85805, 375138172555], 'label': '77760.bo.3240.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.g1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056079
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.g2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.w2', '1620.e2', '1620.l1', '1620.m1', '1620.u1', '1620.ck2'], 'contains': ['6480.e1', '6480.h1', '6480.cl2', '6480.cn2', '6480.ec2', '9720.c2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [179012, 5309, 448908284158, 442641341252], 'label': '77760.bo.3240.g2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.g2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.g2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056080
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.a1', '1080.x1', '1620.a1', '1620.f1', '1620.l1', '1620.n1', '1620.cl1'], 'contains': ['6480.e1', '6480.db1', '6480.dg1', '9720.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [179012, 443120204612, 267845678885, 5309], 'label': '77760.bo.3240.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056081
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.d1', '1080.y1', '1620.a1', '1620.g1', '1620.m1', '1620.o1', '1620.p1', '1620.y1', '1620.cm1'], 'contains': ['6480.e1', '6480.dc1', '6480.de1', '9720.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [88695170185, 143975, 40585, 482670985], 'label': '77760.bo.3240.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.i1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056082
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.e1', '1080.z1', '1620.b1', '1620.d1', '1620.l1', '1620.v1', '1620.cm1'], 'contains': ['6480.e1', '6480.dd1', '6480.df1', '9720.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [5161, 482635561, 224515, 88695348625], 'label': '77760.bo.3240.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.j1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056083
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.b1', '30.c1', '45.a1'], 'contains': ['180.d1', '180.e1', '180.o1', '180.dq1', '180.dz1', '180.ee1', '180.ey1', '270.c1', '270.o1', '270.p1', '360.k1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 80787, 461841009961, 462320328241, 19679028004, 262496684612, 448908283441, 40349], 'label': '77760.bo.90.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '90.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.c1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246056084
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.b1', '1080.ba1', '1620.b1', '1620.c1', '1620.m1', '1620.r1', '1620.cl1'], 'contains': ['6480.e1', '6480.dh1', '6480.di1', '9720.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [443120169575, 267845679358, 143975, 40585], 'label': '77760.bo.3240.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.k1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056085
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.bb1', '1620.c1', '1620.e1', '1620.e2', '1620.n1', '1620.p1', '1620.v1', '1620.cn1'], 'contains': ['6480.e1', '6480.k1', '6480.cr1', '6480.ct1', '6480.eh1', '9720.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [179012, 268244524800, 5309, 274468095480], 'label': '77760.bo.3240.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.l1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056086
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['324.b1', '810.k1', '1080.g1', '1080.i1', '1080.bc1', '1080.bd1', '1620.ba1'], 'contains': ['6480.f1', '6480.g1', '6480.i1', '6480.dn1', '6480.do1', '6480.dx1', '6480.ea1', '9720.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 6480, 'diagramx': None, 'generators': [368871234955, 85946, 174436501946, 375138172555], 'label': '77760.bo.3240.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1620.ba1', 'old_label': '3240.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.m1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056087
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.h1', '1080.be1', '1620.f1', '1620.h1', '1620.r1', '1620.u1', '1620.v1', '1620.y1', '1620.cn1'], 'contains': ['6480.e1', '6480.cp1', '6480.dq1', '9720.i1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [274467916800, 268244524800, 143975, 85805], 'label': '77760.bo.3240.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '3240.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.n1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056088
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.c1', '1080.h1', '1080.bf1', '1080.bh1', '1620.i1', '1620.k1', '1620.q1', '1620.s1', '1620.w1', '1620.z1', '1620.bb1'], 'contains': ['6480.ds1', '9720.i1', '12960.b1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [183845, 274467916800, 268244524800, 194518195200], 'label': '77760.bo.3240.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '3240.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.o1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056089
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.h1', '1080.bg1', '1620.j1', '1620.t1', '1620.x1'], 'contains': ['6480.du1', '9720.i1', '12960.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [442681124645, 183845, 355499204645, 355419268080], 'label': '77760.bo.3240.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1', 'old_label': '3240.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.p1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056090
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['810.l1', '1080.l1', '1080.bi1', '1080.bl1', '1620.ba1'], 'contains': ['6480.b1', '6480.g1', '6480.n1', '6480.z1', '6480.be1', '9720.j1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [518918400, 442641024000, 85805, 143304], 'label': '77760.bo.3240.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1620.ba1', 'old_label': '3240.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.q1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056091
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['810.m1', '1080.l1', '1080.bj1', '1080.bm1', '1620.ba1'], 'contains': ['6480.d1', '6480.i1', '6480.n1', '6480.bb1', '6480.bg1', '9720.j1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [188331234504, 85805, 375138172205, 143304], 'label': '77760.bo.3240.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.j1', 'old_label': '3240.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.r1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056092
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.c1', '810.n1', '1080.m1', '1080.bk1', '1080.bn1', '1620.ba1'], 'contains': ['6480.f1', '6480.l1', '6480.n1', '6480.bd1', '6480.bj1', '9720.k1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [442637395200, 40585, 368392188092, 693], 'label': '77760.bo.3240.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1620.ba1', 'old_label': '3240.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.s1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056093
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.n1', '1080.s1', '1080.bo1', '1620.bj1', '1620.bj2', '1620.ck1'], 'contains': ['6480.p1', '6480.s1', '6480.u1', '6480.br1', '6480.by1', '6480.ec1', '6480.ed1', '9720.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [442641386187, 183845, 143975, 443120026293], 'label': '77760.bo.3240.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bd1', 'old_label': '3240.t1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.t1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056094
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.c1', '30.d1', '45.a1'], 'contains': ['180.j1', '180.k1', '180.o1', '180.eo1', '180.er1', '180.ez1', '180.fa1', '270.d1', '270.r1', '270.t1', '360.n1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 80787, 375138172555, 355462773149, 87661059842, 482635561, 462320328958, 40349], 'label': '77760.bo.90.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '90.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.d1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246056095
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.t2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.bo2', '1620.bj1', '1620.bj2', '1620.ck2'], 'contains': ['6480.p1', '6480.s1', '6480.u1', '6480.br2', '6480.by2', '6480.ec2', '6480.ed2', '9720.a2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [45363, 448908001949, 442641341252, 5066], 'label': '77760.bo.3240.t2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.t2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.t2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056096
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.bc1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.o1', '1080.p1', '1080.q1', '1080.t1', '1080.bo1', '1620.bl1', '1620.bl2', '1620.co1'], 'contains': ['6480.o1', '6480.t1', '6480.v1', '6480.bs1', '6480.bx1', '6480.dz1', '6480.eg1', '9720.a1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [442641024000, 443120071554, 85805, 80787], 'label': '77760.bo.3240.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bi1', 'old_label': '3240.u1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.u1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056097
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.u2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.p1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.o2', '1080.bo2', '1620.bl1', '1620.bl2', '1620.co2'], 'contains': ['6480.o1', '6480.t1', '6480.v1', '6480.bs2', '6480.bx2', '6480.dz2', '6480.eg2', '9720.a2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [40349, 442641386852, 448908001949, 80787], 'label': '77760.bo.3240.u2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.u2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.u2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056098
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.ec1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.r1', '1080.u1', '1080.bp1', '1620.bh1', '1620.bk1', '1620.bl2', '1620.bm1', '1620.bo1', '1620.bq1', '1620.co1'], 'contains': ['6480.o1', '6480.q1', '6480.bs1', '6480.cd1', '6480.ck1', '9720.b1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87181925066, 85805, 375138172205, 80787], 'label': '77760.bo.3240.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.v1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.v1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056099
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.v2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.r2', '1080.bp2', '1620.bc1', '1620.bd1', '1620.bl1', '1620.bq1', '1620.co2'], 'contains': ['6480.o1', '6480.q1', '6480.bs2', '6480.cd2', '6480.ck2', '9720.b2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [40349, 442641024000, 448908001949, 80787], 'label': '77760.bo.3240.v2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.v2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.v2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056100
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.v1', '1080.bp1', '1620.bg1', '1620.bi1', '1620.bj2', '1620.bn1', '1620.bp1', '1620.br1', '1620.ck1'], 'contains': ['6480.p1', '6480.r1', '6480.bt1', '6480.ce1', '6480.cl1', '9720.b1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [85805, 375138172205, 80880, 87182005805], 'label': '77760.bo.3240.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.w1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.w1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056101
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.w2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.bp2', '1620.be1', '1620.bf1', '1620.bj1', '1620.br1', '1620.ck2'], 'contains': ['6480.p1', '6480.r1', '6480.bt2', '6480.ce2', '6480.cl2', '9720.b2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [442641104880, 448908001949, 85805, 80880], 'label': '77760.bo.3240.w2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.w2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.w2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056102
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.bc1', '1080.bq1', '1620.bi1', '1620.bj1', '1620.bu1', '1620.bv1', '1620.cc1', '1620.cd1', '1620.ck1'], 'contains': ['6480.r1', '6480.s1', '6480.cj1', '6480.cn1', '6480.dw1', '9720.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [85805, 148, 375138172555, 87182005805], 'label': '77760.bo.3240.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.x1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.x1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056103
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.x2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.bq2', '1620.bj2', '1620.bs1', '1620.bt1', '1620.cd1', '1620.ck2'], 'contains': ['6480.r1', '6480.s1', '6480.cj2', '6480.cn2', '6480.dw2', '9720.c2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [45363, 442641341252, 5066, 448908283914], 'label': '77760.bo.3240.x2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.x2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.x2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056104
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.bc1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.w1', '1080.bd1', '1080.bq1', '1620.bk1', '1620.bl1', '1620.by1', '1620.bz1', '1620.ce1', '1620.cf1', '1620.co1'], 'contains': ['6480.q1', '6480.t1', '6480.ck1', '6480.cm1', '6480.dz1', '9720.c1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [87181925066, 85805, 375138172555, 80787], 'label': '77760.bo.3240.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.y1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.y1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056105
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.a1', '30.e1'], 'contains': ['180.a1', '180.b1', '180.c1', '180.f1', '180.i1', '180.m1', '180.p1', '180.q1', '180.cg1', '180.ch1', '180.cm1', '270.e1', '810.bc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [93449082115, 224184, 83462998, 456053154955, 174400128000, 224515, 85946, 180587232000], 'label': '77760.bo.90.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '90.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.e1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246056106
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.y2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.w2', '1080.bq2', '1620.bl2', '1620.bw1', '1620.bx1', '1620.cf1', '1620.co2'], 'contains': ['6480.q1', '6480.t1', '6480.ck2', '6480.cm2', '6480.dz2', '9720.c2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [442641386755, 5309, 448908284158, 80787], 'label': '77760.bo.3240.y2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.y2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.y2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056107
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.dv1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.d1', '1080.x1', '1080.br1', '1620.bc1', '1620.bm1', '1620.bw1', '1620.by1', '1620.cp1'], 'contains': ['6480.q1', '6480.cv1', '6480.cz1', '9720.d1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [443120071204, 5309, 267845397242, 80787], 'label': '77760.bo.3240.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.z1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.z1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056108
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.dv1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.r1', '1080.y1', '1080.bs1', '1620.bc1', '1620.bo1', '1620.bx1', '1620.bz1', '1620.cb1', '1620.ci1', '1620.cq1'], 'contains': ['6480.q1', '6480.cw1', '6480.cy1', '9720.e1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [183845, 482849425, 80787, 88695348625], 'label': '77760.bo.3240.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.ba1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ba1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056109
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.s1', '1080.z1', '1080.bt1', '1620.bd1', '1620.bk1', '1620.bw1', '1620.ch1', '1620.cq1'], 'contains': ['6480.q1', '6480.cx1', '6480.cy1', '9720.f1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [40349, 482635561, 80787, 88695348625], 'label': '77760.bo.3240.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.bb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.bb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056110
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.e1', '1080.ba1', '1080.bu1', '1620.bd1', '1620.bh1', '1620.bx1', '1620.ce1', '1620.cp1'], 'contains': ['6480.q1', '6480.cz1', '6480.da1', '9720.g1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [443120071204, 267845679358, 85805, 80787], 'label': '77760.bo.3240.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.bc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.bc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056111
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.f1', '1080.br1', '1620.be1', '1620.bn1', '1620.bs1', '1620.bu1', '1620.cl1'], 'contains': ['6480.r1', '6480.db1', '6480.dh1', '9720.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [443120025600, 267845397242, 5066, 80880], 'label': '77760.bo.3240.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.bd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.bd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056112
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.t1', '1080.bs1', '1620.be1', '1620.bp1', '1620.bt1', '1620.bv1', '1620.ca1', '1620.cj1', '1620.cm1'], 'contains': ['6480.r1', '6480.dc1', '6480.df1', '9720.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [482849425, 219025, 143975, 88695348625], 'label': '77760.bo.3240.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.be1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.be1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056113
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.u1', '1080.bt1', '1620.bf1', '1620.bi1', '1620.bs1', '1620.cg1', '1620.cm1'], 'contains': ['6480.r1', '6480.dd1', '6480.de1', '9720.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [482635561, 40585, 80880, 88695348625], 'label': '77760.bo.3240.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.bf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.bf1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056114
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.g1', '1080.bu1', '1620.bf1', '1620.bg1', '1620.bt1', '1620.cc1', '1620.cl1'], 'contains': ['6480.r1', '6480.dg1', '6480.di1', '9720.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [267845679213, 443120025600, 45363, 85805], 'label': '77760.bo.3240.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.bg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.bg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056115
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.bv1', '1620.bg1', '1620.bj1', '1620.bj2', '1620.bu1', '1620.ca1', '1620.cg1', '1620.cn1'], 'contains': ['6480.r1', '6480.u1', '6480.cp1', '6480.ct1', '6480.eh1', '9720.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [268244605680, 85805, 80880, 274468095480], 'label': '77760.bo.3240.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.bh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.bh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056116
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1', '30.e1'], 'contains': ['180.g1', '180.h1', '180.n1', '180.r1', '180.s1', '180.bz1', '180.ca1', '180.cb1', '270.e1', '810.bh1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [80787, 174400208787, 93448938387, 180587232000, 456053154955, 45813, 83543730, 40349], 'label': '77760.bo.90.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '90.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.f1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246056117
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.bc1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.bb1', '1080.bv1', '1620.bh1', '1620.bl1', '1620.bl2', '1620.by1', '1620.cb1', '1620.ch1', '1620.cr1'], 'contains': ['6480.q1', '6480.v1', '6480.cq1', '6480.cs1', '6480.ei1', '9720.h1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [274468060348, 5309, 268244605587, 80787], 'label': '77760.bo.3240.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.bi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.bi1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056118
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.ec1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.be1', '1080.bf1', '1080.bg1', '1080.bw1', '1620.bm1', '1620.bq1', '1620.ce1', '1620.cf1', '1620.ch1', '1620.ci1', '1620.cr1'], 'contains': ['6480.q1', '6480.cq1', '6480.dp1', '9720.i1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [355499061242, 442680946109, 5309, 80787], 'label': '77760.bo.3240.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '3240.bj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.bj1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056119
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.bh1', '1080.bw1', '1620.bn1', '1620.br1', '1620.cc1', '1620.cd1', '1620.cg1', '1620.cj1', '1620.cn1'], 'contains': ['6480.r1', '6480.cr1', '6480.dq1', '9720.i1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [183845, 274467916800, 268244524800, 143975], 'label': '77760.bo.3240.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '3240.bk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.bk1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056120
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.bi1', '1080.bj1', '1080.bx1', '1620.ck1', '1620.ck2'], 'contains': ['6480.a1', '6480.h1', '6480.p1', '6480.s1', '6480.w1', '6480.bl1', '6480.bp1', '9720.j1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [442641386187, 143975, 85805, 143304], 'label': '77760.bo.3240.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '3240.bl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.bl1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056121
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.h1', '1080.bk1', '1080.by1', '1620.ck1', '1620.ck2', '1620.cl1', '1620.cm1', '1620.cn1'], 'contains': ['6480.e1', '6480.k1', '6480.r1', '6480.u1', '6480.w1', '6480.bn1', '6480.bq1', '9720.k1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [274467916800, 143975, 85805, 143304], 'label': '77760.bo.3240.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.bm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.bm1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056122
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.bl1', '1080.bm1', '1080.bx1', '1620.co1', '1620.co2'], 'contains': ['6480.o1', '6480.t1', '6480.x1', '6480.y1', '6480.bf1', '9720.j1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [85805, 375138172205, 80787, 143304], 'label': '77760.bo.3240.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '3240.bn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.bn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056123
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.i1', '1080.bn1', '1080.by1', '1620.co1', '1620.co2', '1620.cp1', '1620.cq1', '1620.cr1'], 'contains': ['6480.q1', '6480.v1', '6480.x1', '6480.bc1', '6480.bi1', '9720.k1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [274467962404, 85805, 80787, 143304], 'label': '77760.bo.3240.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.bo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.bo1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056124
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.bz1', '1080.ca1', '1080.ck1', '1620.co1', '1620.cs1', '1620.cs2'], 'contains': ['6480.y1', '6480.bf1', '6480.bi1', '6480.bs1', '6480.dz1', '9720.l1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [443120066185, 442641024000, 80787, 143304], 'label': '77760.bo.3240.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bi1', 'old_label': '3240.bp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.bp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056125
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.bp2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.ck2', '1620.co2', '1620.cs1', '1620.cs2'], 'contains': ['6480.y1', '6480.bf1', '6480.bi1', '6480.bs2', '6480.dz2', '9720.l2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [442641109946, 317399, 448908278999, 80787], 'label': '77760.bo.3240.bp2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.bp2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.bp2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056126
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['810.bo1', '1080.bz1', '1080.cc1', '1080.cl1', '1620.ba1'], 'contains': ['6480.z1', '6480.bg1', '6480.bj1', '6480.bu1', '6480.ea1', '9720.l1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [224184, 518918400, 442641024000, 997960349], 'label': '77760.bo.3240.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1620.ba1', 'old_label': '3240.bq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.bq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056127
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['45.b1'], 'contains': ['180.t1', '180.x1', '180.bg1', '180.bh1', '180.bi1', '180.dg1', '180.dj1', '180.dl1', '180.eg1', '180.eh1', '180.ek1', '270.f1', '270.ba1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [143975, 80787, 461841188401, 85805, 19678982548, 448908283914, 80880, 462320328386], 'label': '77760.bo.90.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '90.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.g1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246056128
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['810.bp1', '1080.bz1', '1080.cb1', '1080.cm1'], 'contains': ['6480.ba1', '6480.bh1', '6480.bk1', '6480.bv1', '6480.eb1', '9720.l1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 6480, 'diagramx': None, 'generators': [518964004, 224184, 442641024000, 997960349], 'label': '77760.bo.3240.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3240.br1', 'old_label': '3240.br1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.br1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056129
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.cz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.cd1', '1080.cn1', '1080.co1', '1620.co1', '1620.cs2', '1620.ct1', '1620.cu1', '1620.cx1', '1620.cy1', '1620.cz1'], 'contains': ['6480.y1', '6480.bc1', '6480.bx1', '6480.cd1', '6480.cm1', '9720.m1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [362615, 87182202116, 80787, 375138086400], 'label': '77760.bo.3240.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.bs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.bs1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056130
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.bs2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.cn2', '1080.co2', '1620.co2', '1620.cs1', '1620.cv1', '1620.cw1', '1620.cz1'], 'contains': ['6480.y1', '6480.bc1', '6480.bx2', '6480.cd2', '6480.cm2', '9720.m2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [317399, 448908278999, 442641024000, 80787], 'label': '77760.bo.3240.bs2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.bs2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.bs2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056131
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['810.bq1', '1080.ca1', '1080.cb1', '1080.cc1', '1080.cp1', '1620.ba1'], 'contains': ['6480.bb1', '6480.be1', '6480.bj1', '6480.cg1', '6480.dx1', '9720.l1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [178680, 518918400, 997920000, 442641109705], 'label': '77760.bo.3240.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1620.ba1', 'old_label': '3240.bt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.bt1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056132
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.f1', '810.bs1', '1080.cd1', '1080.ce1', '1080.cq1', '1080.cr1', '1620.ba1'], 'contains': ['6480.z1', '6480.bb1', '6480.bd1', '6480.ca1', '6480.ch1', '6480.ci1', '6480.do1', '9720.m1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [224184, 368871148800, 174436640184, 375138086400], 'label': '77760.bo.3240.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '3240.bu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.bu1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056133
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.cf1', '1080.cs1', '1620.co1', '1620.cs1', '1620.ct1', '1620.dd1', '1620.dg1', '1620.dj1', '1620.dm1'], 'contains': ['6480.bc1', '6480.bf1', '6480.ck1', '6480.eg1', '9720.n1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [362615, 87182202116, 375138172205, 80787], 'label': '77760.bo.3240.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.bv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.bv1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056134
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.bv2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.cs2', '1620.co2', '1620.cs2', '1620.de1', '1620.df1', '1620.dm1'], 'contains': ['6480.bc1', '6480.bf1', '6480.ck2', '6480.eg2', '9720.n2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [282215, 448908284158, 442641109705, 80787], 'label': '77760.bo.3240.bv2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.bv2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.bv2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056135
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.ct1', '1620.cr1', '1620.cs1', '1620.cs2', '1620.cu1', '1620.dd1', '1620.dh1', '1620.dn1'], 'contains': ['6480.bc1', '6480.bi1', '6480.cq1', '6480.ei1', '9720.o1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [178680, 268244605587, 274468002505, 80787], 'label': '77760.bo.3240.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.bw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.bw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056136
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.cv1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.j1', '1080.cu1', '1080.cy1', '1620.cp1', '1620.cv1', '1620.cx1', '1620.dd1', '1620.de1'], 'contains': ['6480.bc1', '6480.cv1', '6480.da1', '9720.p1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [443120071204, 282215, 80787, 267845674052], 'label': '77760.bo.3240.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.bx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.bx1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056137
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.cv1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.bx1', '1080.cv1', '1080.cz1', '1620.cq1', '1620.cv1', '1620.cy1', '1620.df1', '1620.dg1', '1620.dh1', '1620.dq1'], 'contains': ['6480.bc1', '6480.cw1', '6480.cx1', '9720.q1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [482854444, 88695353644, 80787, 143304], 'label': '77760.bo.3240.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.by1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.by1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056138
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['30.b1', '45.b1'], 'contains': ['180.w1', '180.x2', '180.y1', '180.be1', '180.bg1', '180.bn1', '180.bq1', '180.dg2', '180.dh1', '180.dm1', '180.dn1', '180.eh1', '180.ei1', '180.en1', '180.eu1', '270.g1', '270.bb1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 80787, 461841188401, 85805, 462320328958, 19678982548, 448908283914, 80880], 'label': '77760.bo.90.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '90.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.h1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246056139
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.y1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.by1', '1080.cw1', '1620.cq1', '1620.ct1', '1620.cw1', '1620.de1', '1620.dn1'], 'contains': ['6480.bc1', '6480.cy1', '9720.r1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [482808988, 224184, 80787, 88695348625], 'label': '77760.bo.3240.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.bz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.bz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056140
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.y1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.k1', '1080.cx1', '1620.cp1', '1620.cu1', '1620.cw1', '1620.df1', '1620.dj1'], 'contains': ['6480.bc1', '6480.cz1', '9720.s1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [443120071204, 362615, 267845679358, 80787], 'label': '77760.bo.3240.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.ca1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ca1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056141
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.g1', '810.bu1', '1080.cf1', '1080.ch1', '1080.da1', '1620.ba1'], 'contains': ['6480.bd1', '6480.be1', '6480.bg1', '6480.dn1', '6480.ee1', '9720.n1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [375138091561, 224184, 368871153961, 174436640184], 'label': '77760.bo.3240.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1620.ba1', 'old_label': '3240.cb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cb1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056142
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.cz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.cg1', '1080.db1', '1080.dc1', '1620.cr1', '1620.cx1', '1620.cz1', '1620.dj1', '1620.dm1', '1620.dn1', '1620.dq1'], 'contains': ['6480.bc1', '6480.cs1', '6480.dp1', '9720.t1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [274467962404, 268244605587, 80787, 143304], 'label': '77760.bo.3240.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '3240.cc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056143
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.l1', '1080.cg1', '1080.dd1', '1080.df1', '1620.bb1', '1620.da1', '1620.dc1', '1620.di1', '1620.dk1', '1620.do1', '1620.dr1'], 'contains': ['6480.ds1', '9720.t1', '12960.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [274467916800, 268244524800, 194518195200, 143304], 'label': '77760.bo.3240.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '3240.cd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cd1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056144
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.cg1', '1080.de1', '1080.dg1', '1620.db1', '1620.dl1', '1620.dp1'], 'contains': ['6480.dt1', '9720.t1', '12960.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [442681258052, 355419549955, 355499020800, 317252], 'label': '77760.bo.3240.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bl1', 'old_label': '3240.ce1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ce1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056145
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.ck1', '1080.cl1', '1080.cm1', '1080.cp1', '1620.ck1', '1620.ds1', '1620.ds2'], 'contains': ['6480.bl1', '6480.bp1', '6480.bq1', '6480.br1', '6480.bt1', '6480.dw1', '6480.ec1', '9720.l1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [143975, 375138270474, 87182197050, 143304], 'label': '77760.bo.3240.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bd1', 'old_label': '3240.cf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cf1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056146
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cf2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.ck2', '1620.ck2', '1620.ds1', '1620.ds2'], 'contains': ['6480.bl1', '6480.bp1', '6480.bq1', '6480.br2', '6480.bt2', '6480.dw2', '6480.ec2', '9720.l2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [362615, 45363, 442641069363, 448908283914], 'label': '77760.bo.3240.cf2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.cf2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cf2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056147
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.bq1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.cn1', '1080.cq1', '1620.ck1', '1620.ds2', '1620.dt1', '1620.du1', '1620.dy1', '1620.ea1', '1620.ec1'], 'contains': ['6480.bl1', '6480.bn1', '6480.by1', '6480.ce1', '6480.cn1', '9720.m1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [442641104880, 443120025600, 80880, 143304], 'label': '77760.bo.3240.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.cg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056148
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cg2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.cn2', '1620.ck2', '1620.ds1', '1620.dv1', '1620.dw1', '1620.ec1'], 'contains': ['6480.bl1', '6480.bn1', '6480.by2', '6480.ce2', '6480.cn2', '9720.m2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [224184, 224515, 448908243571, 442641305788], 'label': '77760.bo.3240.cg2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.cg2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cg2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056149
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['45.b1'], 'contains': ['180.v1', '180.x2', '180.z1', '180.bf1', '180.bi1', '180.dg2', '180.di1', '180.do1', '180.dp1', '180.ej1', '180.ek1', '270.h1', '270.bc1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [143975, 80787, 461841188401, 85805, 462320328958, 19678982548, 448908283441, 80880], 'label': '77760.bo.90.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '90.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.i1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246056150
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.co1', '1080.cr1', '1620.dz1', '1620.eb1', '1620.ed1'], 'contains': ['6480.bm1', '6480.bo1', '6480.bz1', '6480.cf1', '6480.co1', '9720.m1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [442641305544, 143731, 443120169331, 143304], 'label': '77760.bo.3240.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '3240.ch1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ch1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056151
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ch2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.co2', '1620.dx1', '1620.ed1'], 'contains': ['6480.bm1', '6480.bo1', '6480.bz2', '6480.cf2', '6480.co2', '9720.m2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [442641305544, 143731, 448908243571, 143304], 'label': '77760.bo.3240.ch2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '3240.ch2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ch2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056152
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.cs1', '1080.da1', '1620.ck1', '1620.ds1', '1620.dt1', '1620.ee1', '1620.eh1', '1620.ej1', '1620.ek1'], 'contains': ['6480.bn1', '6480.bp1', '6480.cj1', '6480.cl1', '6480.ed1', '9720.n1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [362615, 45363, 375138172205, 87182282615], 'label': '77760.bo.3240.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.ci1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ci1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056153
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ci2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.cs2', '1620.ck2', '1620.ds2', '1620.ef1', '1620.eg1', '1620.ek1'], 'contains': ['6480.bn1', '6480.bp1', '6480.cj2', '6480.cl2', '6480.ed2', '9720.n2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [362615, 45363, 442641109705, 448908283914], 'label': '77760.bo.3240.ci2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.ci2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ci2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056154
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.ct1', '1620.cn1', '1620.ds1', '1620.ds2', '1620.du1', '1620.ee1', '1620.ei1', '1620.el1'], 'contains': ['6480.bn1', '6480.bq1', '6480.cp1', '6480.cr1', '6480.eh1', '9720.o1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [274468002505, 268244605680, 80880, 143304], 'label': '77760.bo.3240.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.cj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056155
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.m1', '1080.cu1', '1620.cl1', '1620.dv1', '1620.dy1', '1620.ee1', '1620.ef1'], 'contains': ['6480.bn1', '6480.db1', '6480.di1', '9720.p1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [179012, 178680, 443120204612, 267845674052], 'label': '77760.bo.3240.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.ck1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ck1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056156
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.cl1', '1080.cv1', '1620.cm1', '1620.dv1', '1620.ea1', '1620.eg1', '1620.eh1', '1620.ei1', '1620.em1'], 'contains': ['6480.bn1', '6480.dc1', '6480.dd1', '9720.q1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [143975, 88695272904, 482773704, 143304], 'label': '77760.bo.3240.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.cl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056157
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.cm1', '1080.cw1', '1620.cm1', '1620.dt1', '1620.dw1', '1620.ef1', '1620.el1'], 'contains': ['6480.bn1', '6480.de1', '6480.df1', '9720.r1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [482854584, 224184, 224515, 88695348625], 'label': '77760.bo.3240.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.cm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056158
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.n1', '1080.cx1', '1620.cl1', '1620.du1', '1620.dw1', '1620.eg1', '1620.ej1'], 'contains': ['6480.bn1', '6480.dg1', '6480.dh1', '9720.s1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [362615, 267845679213, 443120025600, 45363], 'label': '77760.bo.3240.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.cn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056159
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.o1', '1080.cy1', '1620.dx1', '1620.dz1'], 'contains': ['6480.bo1', '6480.dj1', '6480.dm1', '9720.p1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [443120250212, 224184, 267845674052, 224612], 'label': '77760.bo.3240.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '3240.co1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.co1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056160
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['30.a1', '45.a1'], 'contains': ['180.ba1', '180.bk1', '180.bo1', '180.dq1', '180.du1', '180.eo1', '180.es1', '270.i1', '270.k1', '270.bd1', '360.z1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 80787, 19679028004, 462320328958, 262496684612, 461841223825, 448908283441, 183845], 'label': '77760.bo.90.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '90.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.j1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246056161
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.cn1', '1080.cz1', '1620.dx1', '1620.eb1', '1620.en1'], 'contains': ['6480.bo1', '6480.dk1', '6480.dl1', '9720.q1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [143731, 88695272904, 482773704, 143304], 'label': '77760.bo.3240.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '3240.cp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cp1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056162
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.bq1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.db1', '1080.dd1', '1080.de1', '1620.cn1', '1620.dy1', '1620.ec1', '1620.ej1', '1620.ek1', '1620.el1', '1620.em1'], 'contains': ['6480.bn1', '6480.ct1', '6480.dq1', '9720.t1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [442681119480, 179012, 178680, 355499199812], 'label': '77760.bo.3240.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '3240.cq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056163
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.dc1', '1080.df1', '1080.dg1', '1620.dz1', '1620.ed1', '1620.en1'], 'contains': ['6480.bo1', '6480.cu1', '6480.dr1', '9720.t1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [274467916800, 268244524800, 143731, 143304], 'label': '77760.bo.3240.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '3240.cr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cr1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056164
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.dh1', '1620.e1', '1620.bj2', '1620.ds2'], 'contains': ['6480.br2', '6480.bt1', '6480.by1', '6480.dw2', '6480.ec1', '6480.ed2', '6480.eh1', '9720.u1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [19679206584, 224515, 448908243571, 462320328958], 'label': '77760.bo.3240.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bd1', 'old_label': '3240.cs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cs1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056165
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cs2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.dh2', '1620.e2', '1620.bj1', '1620.ds2'], 'contains': ['6480.br1', '6480.bt2', '6480.by1', '6480.dw1', '6480.ec2', '6480.ed2', '6480.eh1', '9720.u1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [19679299652, 45363, 448908243571, 462320328958], 'label': '77760.bo.3240.cs2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bd1', 'old_label': '3240.cs2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cs2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056166
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cs3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.dh3', '1620.e1', '1620.bj1', '1620.ds1'], 'contains': ['6480.br2', '6480.bt2', '6480.by2', '6480.dw1', '6480.ec1', '6480.ed1', '6480.eh1', '9720.u2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [19679161080, 461841090505, 179012, 462320323320], 'label': '77760.bo.3240.cs3', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bd1', 'old_label': '3240.cs3', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cs3', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056167
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cs4', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.dh4', '1620.e2', '1620.bj2', '1620.ds1'], 'contains': ['6480.br1', '6480.bt1', '6480.by2', '6480.dw2', '6480.ec2', '6480.ed1', '6480.eh1', '9720.u3'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [19679161080, 461841090505, 179012, 462320323652], 'label': '77760.bo.3240.cs4', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bd1', 'old_label': '3240.cs4', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cs4', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056168
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.bc1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.dh1', '1080.dh2', '1620.bl1', '1620.bl2', '1620.cs2'], 'contains': ['6480.bs1', '6480.bs2', '6480.bx1', '6480.dz1', '6480.dz2', '6480.eg2', '6480.ei1', '9720.u1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [461841090505, 462320046842, 19679125948, 80787], 'label': '77760.bo.3240.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bi1', 'old_label': '3240.ct1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ct1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056169
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ct2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.dh3', '1620.bl1', '1620.cs1'], 'contains': ['6480.bs2', '6480.bx2', '6480.dz1', '6480.eg1', '6480.ei1', '9720.u2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [19679068105, 448908284158, 462320046842, 80787], 'label': '77760.bo.3240.ct2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bi1', 'old_label': '3240.ct2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ct2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056170
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ct3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.dh4', '1620.bl2', '1620.cs1'], 'contains': ['6480.bs1', '6480.bx2', '6480.dz2', '6480.eg1', '6480.ei1', '9720.u3'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841090505, 19679125948, 80787, 462320230347], 'label': '77760.bo.3240.ct3', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bi1', 'old_label': '3240.ct3', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ct3', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056171
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': ['9720.a1', '9720.j1', '9720.l1', '9720.a2', '9720.u1', '9720.u2', '9720.u3', '9720.l2'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1'], 'contains': ['24.a1', '24.g1', '48.a1', '80.o1', '120.cc1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [143975, 87182201788, 274511507904, 80880, 80787], 'label': '77760.bo.8.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1'], 'normal_contains': ['24.a1', '2880.a1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '77760.bo', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '25920.w'}
  • id: 246056172
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['30.a1'], 'contains': ['180.bb1', '180.bl1', '180.bp1', '180.dr1', '180.dv1', '180.ep1', '180.et1', '270.l1', '270.bd1', '360.ba1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [183845, 355462871189, 87661059842, 482635561, 143975, 462320328958, 375138172555, 80787], 'label': '77760.bo.90.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.k1', 'old_label': '90.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.k1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
  • id: 246056173
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.di1', '1620.h1', '1620.bj1', '1620.ds1', '1620.eo1', '1620.er1', '1620.ez1', '1620.ft1'], 'contains': ['6480.br1', '6480.br2', '6480.ce2', '6480.cj1', '6480.cp1', '9720.v1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [19679063280, 461841188401, 462320006400, 80880], 'label': '77760.bo.3240.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.cu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cu1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056174
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cu2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.di2', '1620.h1', '1620.bj2', '1620.ds2', '1620.eq1', '1620.ex1', '1620.fh1', '1620.fn1'], 'contains': ['6480.br1', '6480.br2', '6480.ce1', '6480.cj2', '6480.cp1', '9720.v2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841090505, 179012, 19678982400, 462320363665], 'label': '77760.bo.3240.cu2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.cu2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cu2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056175
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.d2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.dq1', '1080.dj1', '1620.g1', '1620.bi1', '1620.dt1', '1620.ep1', '1620.ey1', '1620.fh1', '1620.ft1'], 'contains': ['6480.ce1', '6480.cj1', '6480.de1', '9720.w1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [87261753748, 456053069043, 83467916, 148], 'label': '77760.bo.3240.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.cv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cv1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246056176
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.ec1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.di1', '1080.dk1', '1620.bl1', '1620.bq1', '1620.cs1', '1620.es1', '1620.fb1', '1620.fc1', '1620.fu1'], 'contains': ['6480.bs1', '6480.bs2', '6480.cd2', '6480.ck1', '6480.cq1', '9720.v1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [19679304958, 448908284158, 462320328958, 80787], 'label': '77760.bo.3240.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.cw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056177
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cw2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.ec1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.di2', '1080.dk2', '1620.bl2', '1620.bq1', '1620.cs2', '1620.et1', '1620.fa1', '1620.fi1', '1620.fo1'], 'contains': ['6480.bs1', '6480.bs2', '6480.cd1', '6480.ck2', '6480.cq1', '9720.v2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [448908007204, 19679028004, 462320328958, 80787], 'label': '77760.bo.3240.cw2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.cw2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cw2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056178
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.dk1', '1620.e1', '1620.br1', '1620.ds1', '1620.ev1', '1620.ez1', '1620.fd1', '1620.fv1'], 'contains': ['6480.bt1', '6480.bt2', '6480.ce2', '6480.cl1', '6480.cr1', '9720.v1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841223825, 179012, 19678982400, 462320323320], 'label': '77760.bo.3240.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.cx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056179
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cx2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.dk2', '1620.e2', '1620.br1', '1620.ds2', '1620.ew1', '1620.ey1', '1620.fj1', '1620.fp1'], 'contains': ['6480.bt1', '6480.bt2', '6480.ce1', '6480.cl2', '6480.cr1', '9720.v2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [19679063280, 461841090505, 80880, 462320046985], 'label': '77760.bo.3240.cx2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.cx2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cx2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056180
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.cg2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.dr1', '1080.dj1', '1080.dl1', '1620.bk1', '1620.bo1', '1620.ct1', '1620.es2', '1620.fa1', '1620.fi1', '1620.fu1'], 'contains': ['6480.cd1', '6480.ck1', '6480.cy1', '9720.w1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [456053068800, 83548555, 87261834387, 80787], 'label': '77760.bo.3240.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.cy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056181
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.ds1', '1080.dl1', '1620.d1', '1620.bp1', '1620.dt1', '1620.eu1', '1620.ex1', '1620.fj1', '1620.fv1'], 'contains': ['6480.ce1', '6480.cl1', '6480.df1', '9720.w1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [87261834480, 83507904, 456053073961, 80880], 'label': '77760.bo.3240.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.cz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.cz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056182
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.cz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.dm1', '1080.dn1', '1620.bl1', '1620.cz1', '1620.es1', '1620.fe1', '1620.fz1'], 'contains': ['6480.bx1', '6480.bx2', '6480.cd2', '6480.cm1', '6480.cs1', '9720.x1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [19679028004, 462320052004, 461841148348, 80787], 'label': '77760.bo.3240.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.da1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.da1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056183
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['30.a1', '45.b1'], 'contains': ['180.u1', '180.v1', '180.w1', '180.x1', '180.bc1', '180.bm1', '180.bq1', '180.dg1', '180.dh1', '180.di1', '180.dk1', '180.ds1', '180.dw1', '180.eq1', '180.eu1', '270.j1', '270.bd1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [183845, 448908283441, 143975, 19678982548, 461841188401, 462320328958, 80880, 80787], 'label': '77760.bo.90.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '90.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.l1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246056184
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.da2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.cz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.dm2', '1080.dn2', '1620.bl2', '1620.cz1', '1620.es2', '1620.fk1', '1620.fq1'], 'contains': ['6480.bx1', '6480.bx2', '6480.cd1', '6480.cm2', '6480.cs1', '9720.x2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [19679028004, 461841148348, 80787, 462320230347], 'label': '77760.bo.3240.da2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.da2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.da2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056185
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bs2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.dt1', '1080.do1', '1080.dp1', '1620.bk1', '1620.cy1', '1620.et1', '1620.fk1', '1620.fz1'], 'contains': ['6480.cd1', '6480.cm1', '6480.cx1', '9720.y1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [456053150130, 83462400, 87261834387, 80787], 'label': '77760.bo.3240.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.db1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.db1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246056186
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.bq1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.dm1', '1620.e1', '1620.bj1', '1620.ec1', '1620.eo1', '1620.ev1', '1620.ff1', '1620.ga1'], 'contains': ['6480.by1', '6480.by2', '6480.ce2', '6480.cn1', '6480.ct1', '9720.x1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [45363, 448908243571, 462320006400, 19679027763], 'label': '77760.bo.3240.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.dc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.dc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056187
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.dc2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.bq1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.dm2', '1620.e2', '1620.bj2', '1620.ec1', '1620.ep1', '1620.eu1', '1620.fl1', '1620.fr1'], 'contains': ['6480.by1', '6480.by2', '6480.ce1', '6480.cn2', '6480.ct1', '9720.x2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [19679299652, 45363, 448908243571, 462320006400], 'label': '77760.bo.3240.dc2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.dc2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.dc2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056188
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.dn1', '1620.ed1', '1620.fg1', '1620.gb1'], 'contains': ['6480.bz1', '6480.bz2', '6480.cf2', '6480.co1', '6480.cu1', '9720.x1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [462320368684, 461841183480, 19678982400, 179159], 'label': '77760.bo.3240.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '3240.dd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.dd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056189
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.dd2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.dn2', '1620.ed1', '1620.fm1', '1620.fs1'], 'contains': ['6480.bz1', '6480.bz2', '6480.cf1', '6480.co2', '6480.cu1', '9720.x2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [462320287944, 143731, 448908243571, 19679125704], 'label': '77760.bo.3240.dd2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '3240.dd2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.dd2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056190
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.v2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.du1', '1080.do1', '1620.d1', '1620.bi1', '1620.ea1', '1620.eq1', '1620.ew1', '1620.fl1', '1620.ga1'], 'contains': ['6480.ce1', '6480.cn1', '6480.dd1', '9720.y1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [83462998, 87262035388, 224515, 456053293315], 'label': '77760.bo.3240.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.de1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.de1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056191
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.dv1', '1080.dp1', '1620.eb1', '1620.fm1', '1620.gb1'], 'contains': ['6480.cf1', '6480.co1', '6480.dl1', '9720.y1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87262115884, 83462998, 456053247959, 179159], 'label': '77760.bo.3240.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '3240.df1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.df1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056192
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.d2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.dq1', '1620.f1', '1620.bg1', '1620.du1', '1620.eu1', '1620.ew1', '1620.fn1', '1620.ft1'], 'contains': ['6480.ce1', '6480.cp1', '6480.dg1', '9720.z1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [442641104880, 443120025600, 180667249346, 80880], 'label': '77760.bo.3240.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.dg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.dg1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246056193
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.cg2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.dq1', '1080.dr1', '1620.bh1', '1620.bm1', '1620.cu1', '1620.es2', '1620.et1', '1620.fo1', '1620.fu1'], 'contains': ['6480.cd1', '6480.cq1', '6480.cz1', '9720.z1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [482849425, 80787, 375138086400, 87182000787], 'label': '77760.bo.3240.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.dh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.dh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056194
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['30.b1', '45.a1'], 'contains': ['180.bd1', '180.bj1', '180.bo1', '180.dz1', '180.eb1', '180.er1', '180.ev1', '270.m1', '270.n1', '270.bb1', '360.bd1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [87661007546, 183845, 482635561, 143975, 375138225118, 355462916645, 80787, 462320328241], 'label': '77760.bo.90.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '90.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.m1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246056195
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.dr1', '1620.c1', '1620.bn1', '1620.du1', '1620.ep1', '1620.eq1', '1620.fp1', '1620.fv1'], 'contains': ['6480.ce1', '6480.cr1', '6480.dh1', '9720.z1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [442641386187, 443120169575, 180667203842, 143975], 'label': '77760.bo.3240.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.di1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.di1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056196
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bs2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.ds1', '1080.dt1', '1620.bh1', '1620.cx1', '1620.fa1', '1620.fq1', '1620.fz1'], 'contains': ['6480.cd1', '6480.cs1', '6480.da1', '9720.ba1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [443120071204, 180667209003, 442641024000, 80787], 'label': '77760.bo.3240.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.dj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.dj1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246056197
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.v2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.ds1', '1620.c1', '1620.bg1', '1620.dy1', '1620.ex1', '1620.ey1', '1620.fr1', '1620.ga1'], 'contains': ['6480.ce1', '6480.ct1', '6480.di1', '9720.ba1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [442641104880, 443120025600, 180667289784, 80880], 'label': '77760.bo.3240.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.dk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.dk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056198
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.dt1', '1620.dz1', '1620.fs1', '1620.gb1'], 'contains': ['6480.cf1', '6480.cu1', '6480.dm1', '9720.ba1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87182237067, 482854584, 375138311012, 224612], 'label': '77760.bo.3240.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '3240.dl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.dl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056199
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.cs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.du1', '1080.dy1', '1620.bc1', '1620.cv1', '1620.fb1', '1620.fe1', '1620.gh1'], 'contains': ['6480.cd2', '6480.cv1', '6480.cw1', '9720.bb1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [7185024000, 19679028004, 462320052004, 80787], 'label': '77760.bo.3240.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '3240.dm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.dm1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056200
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.cv1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.dv1', '1080.dz1', '1620.bd1', '1620.cv1', '1620.fc1', '1620.fz1'], 'contains': ['6480.cd2', '6480.cx1', '6480.da1', '9720.bc1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [19679028004, 462320052004, 80787, 7185202680], 'label': '77760.bo.3240.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.dn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.dn1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056201
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.dv1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.dw1', '1080.dx1', '1620.bc1', '1620.bd1', '1620.cw1', '1620.es1', '1620.fu1'], 'contains': ['6480.cd2', '6480.cy1', '6480.cz1', '9720.bd1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [7185029309, 19679028004, 462320052004, 80787], 'label': '77760.bo.3240.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.do1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.do1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056202
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.du1', '1620.a1', '1620.be1', '1620.dv1', '1620.er1', '1620.fd1', '1620.ff1', '1620.gi1'], 'contains': ['6480.ce2', '6480.db1', '6480.dc1', '9720.bb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [19679063280, 7185104880, 462320006400, 80880], 'label': '77760.bo.3240.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.dp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.dp1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056203
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.dv1', '1620.b1', '1620.bf1', '1620.dv1', '1620.ez1', '1620.ga1'], 'contains': ['6480.ce2', '6480.dd1', '6480.di1', '9720.bc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [19679063280, 462320006400, 80880, 7185202680], 'label': '77760.bo.3240.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.dq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.dq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056204
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.dw1', '1620.a1', '1620.bf1', '1620.dw1', '1620.ev1', '1620.ft1'], 'contains': ['6480.ce2', '6480.de1', '6480.dg1', '9720.bd1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [19679063280, 7185162389, 462320006400, 80880], 'label': '77760.bo.3240.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.dr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.dr1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056205
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['30.c1', '45.b1'], 'contains': ['180.t1', '180.y1', '180.z1', '180.bc1', '180.br1', '180.dj1', '180.dm1', '180.do1', '180.ds1', '180.ed1', '180.ew1', '270.o1', '270.be1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [183845, 143975, 19678982548, 461841188401, 462320328958, 80880, 80787, 448908283914], 'label': '77760.bo.90.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '90.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.n1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246056206
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.dx1', '1620.b1', '1620.be1', '1620.dw1', '1620.eo1', '1620.fv1'], 'contains': ['6480.ce2', '6480.df1', '6480.dh1', '9720.bd1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [7185207845, 179012, 19678982400, 462320323320], 'label': '77760.bo.3240.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.ds1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ds1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056207
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.dy1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.dy1', '1620.dx1', '1620.fg1', '1620.gj1'], 'contains': ['6480.cf2', '6480.dj1', '6480.dk1', '9720.bb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [462320368684, 19678982400, 7185024000, 179159], 'label': '77760.bo.3240.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '3240.dt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.dt1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056208
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.dz1', '1620.dx1', '1620.gb1'], 'contains': ['6480.cf2', '6480.dl1', '6480.dm1', '9720.bc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [462320368684, 19678982400, 7185202680, 179159], 'label': '77760.bo.3240.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '3240.du1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.du1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056209
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.cp2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.ea1', '1080.eb1', '1080.en1', '1620.bm1', '1620.cx1', '1620.fi1', '1620.fk1', '1620.gh1'], 'contains': ['6480.cd1', '6480.cv1', '6480.dp1', '9720.be1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [443120071204, 180667146387, 442641024000, 80787], 'label': '77760.bo.3240.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '3240.dv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.dv1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246056210
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.r2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.ea1', '1080.eo1', '1620.f1', '1620.bn1', '1620.dy1', '1620.fh1', '1620.fj1', '1620.fl1', '1620.gi1'], 'contains': ['6480.ce1', '6480.db1', '6480.dq1', '9720.be1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [442641386187, 443120169575, 143975, 180667065600], 'label': '77760.bo.3240.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.dw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.dw1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246056211
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.dk2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.eb1', '1080.ep1', '1620.dz1', '1620.fm1', '1620.gj1'], 'contains': ['6480.cf1', '6480.dj1', '6480.dr1', '9720.be1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [443120204759, 442641386284, 180667065600, 179159], 'label': '77760.bo.3240.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '3240.dx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.dx1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246056212
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.cp2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.dw1', '1080.ec1', '1080.ed1', '1620.bo1', '1620.cy1', '1620.fo1', '1620.fq1', '1620.gh1'], 'contains': ['6480.cd1', '6480.cw1', '9720.bf1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [456053068800, 83462400, 87261834387, 80787], 'label': '77760.bo.3240.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '3240.dy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.dy1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246056213
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.r2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.dx1', '1080.ec1', '1620.g1', '1620.bp1', '1620.ea1', '1620.fn1', '1620.fp1', '1620.fr1', '1620.gi1'], 'contains': ['6480.ce1', '6480.dc1', '9720.bf1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [83606375, 143975, 456053212775, 87262115787], 'label': '77760.bo.3240.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.dz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.dz1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246056214
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.dk2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.dy1', '1080.ed1', '1620.eb1', '1620.fs1', '1620.gj1'], 'contains': ['6480.cf1', '6480.dk1', '9720.bf1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [87262115884, 83641559, 456053247959, 179159], 'label': '77760.bo.3240.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '3240.ea1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ea1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246056215
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.cw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.ee1', '1080.ef1', '1080.eg1', '1080.eh1', '1080.ei1', '1620.bq1', '1620.cz1', '1620.fu1', '1620.fz1', '1620.gh1'], 'contains': ['6480.cd1', '6480.cd2', '6480.dp1', '9720.bg1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [19679028004, 462320052004, 461841050404, 80787], 'label': '77760.bo.3240.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '3240.eb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.eb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056216
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.a1', '30.c1', '45.a1'], 'contains': ['180.ba1', '180.bd1', '180.bs1', '180.dt1', '180.ea1', '180.ee1', '180.ez1', '270.p1', '270.q1', '270.be1', '360.be1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [80787, 87660962042, 85805, 375138172205, 482635561, 355462738109, 80880, 462320046985], 'label': '77760.bo.90.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '90.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.o1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246056217
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.s1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.ee1', '1080.ej1', '1080.ek1', '1620.h1', '1620.br1', '1620.ec1', '1620.ft1', '1620.fv1', '1620.ga1', '1620.gi1'], 'contains': ['6480.ce1', '6480.ce2', '6480.dq1', '9720.bg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [19679063280, 461841085680, 462320006400, 80880], 'label': '77760.bo.3240.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '3240.ec1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ec1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056218
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.ef1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.ef1', '1080.el1', '1080.em1', '1620.ed1', '1620.gb1', '1620.gj1'], 'contains': ['6480.cf1', '6480.cf2', '6480.dr1', '9720.bg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [462320368684, 19678982400, 448908323884, 179159], 'label': '77760.bo.3240.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '3240.ed1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ed1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056219
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.bs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.eg1', '1080.ej1', '1080.el1', '1620.i1', '1620.da1', '1620.fw1', '1620.gc1', '1620.gk1'], 'contains': ['6480.ds1', '9720.bg1', '12960.n1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [355462732800, 87660921600, 462320006400, 375138086400], 'label': '77760.bo.3240.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '3240.ee1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ee1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056220
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.cj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.eg1', '1080.ek1', '1080.em1', '1620.db1', '1620.fx1'], 'contains': ['6480.dt1', '9720.bg1', '12960.o1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [461841004800, 19678982400, 462320006400, 262496586387], 'label': '77760.bo.3240.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.i1', 'old_label': '3240.ef1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ef1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056221
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.eh1', '1080.ej1', '1080.ek1', '1620.j1', '1620.fy1', '1620.gd1'], 'contains': ['6480.du1', '9720.bg1', '12960.p1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [461841004800, 19678982400, 462320006400, 262496505748], 'label': '77760.bo.3240.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1', 'old_label': '3240.eg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.eg1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056222
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.ei1', '1080.el1', '1080.em1', '1620.ge1'], 'contains': ['6480.dv1', '9720.bg1', '12960.q1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [461841004800, 262496649331, 19678982400, 462320006400], 'label': '77760.bo.3240.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.dx1', 'old_label': '3240.eh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.eh1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056223
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.bs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.p1', '1080.en1', '1080.eo1', '1080.ep1', '1620.k1', '1620.dc1', '1620.gf1', '1620.gg1', '1620.gk1'], 'contains': ['6480.ds1', '9720.be1', '12960.r1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [443120025600, 442641024000, 442162022400, 180667065600], 'label': '77760.bo.3240.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '3240.ei1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ei1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056224
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.et1', '1620.e1', '1620.cd1', '1620.ds2', '1620.eq1', '1620.gl1', '1620.gq1', '1620.ha1'], 'contains': ['6480.cj2', '6480.cn1', '6480.cr1', '6480.dw1', '6480.dw2', '9720.bh1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841090505, 45363, 462320363997, 19679027763], 'label': '77760.bo.3240.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.ej1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ej1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056225
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ej2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.et2', '1620.e2', '1620.cd1', '1620.ds1', '1620.ep1', '1620.gm1', '1620.gr1', '1620.gz1'], 'contains': ['6480.cj1', '6480.cn2', '6480.cr1', '6480.dw1', '6480.dw2', '9720.bh2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841223825, 19678982400, 143975, 462320369015], 'label': '77760.bo.3240.ej2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.ej2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ej2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056226
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fv1', '1080.eu1', '1620.d1', '1620.bv1', '1620.dt1', '1620.eo1', '1620.gp1', '1620.gz1', '1620.ha1'], 'contains': ['6480.cj1', '6480.cn1', '6480.df1', '9720.bi1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [87261753748, 456053069398, 83467916, 148], 'label': '77760.bo.3240.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.ek1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ek1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056227
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['30.d1', '45.b1'], 'contains': ['180.bf1', '180.bh1', '180.bm1', '180.bn1', '180.br1', '180.eg1', '180.ej1', '180.en1', '180.eq1', '180.ew1', '180.ex1', '270.r1', '270.bf1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [183845, 448908283441, 143975, 19678982548, 461841188401, 80880, 80787, 462320328386], 'label': '77760.bo.90.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '90.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.p1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246056228
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.d2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.ev1', '1620.f1', '1620.bu1', '1620.ee1', '1620.er1', '1620.fh1', '1620.gp1', '1620.gr1'], 'contains': ['6480.cj1', '6480.cp1', '6480.db1', '9720.bj1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [482716205, 143975, 375138270474, 87182282187], 'label': '77760.bo.3240.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.el1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.el1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246056229
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.ew1', '1620.c1', '1620.cc1', '1620.ee1', '1620.ey1', '1620.ez1', '1620.gm1', '1620.ha1'], 'contains': ['6480.cj1', '6480.cr1', '6480.di1', '9720.bk1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [148, 375138172555, 482716346, 87181920000], 'label': '77760.bo.3240.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.em1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.em1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056230
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.ex1', '1620.c1', '1620.bu1', '1620.ej1', '1620.eo1', '1620.ep1', '1620.gs1', '1620.hh1'], 'contains': ['6480.cj1', '6480.ct1', '6480.dh1', '9720.bl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [143975, 375138270474, 87182282187, 482773704], 'label': '77760.bo.3240.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.en1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.en1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056231
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.ey1', '1620.a1', '1620.bs1', '1620.ef1', '1620.fh1', '1620.gq1'], 'contains': ['6480.cj2', '6480.db1', '6480.de1', '9720.bm1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [19678982400, 7185024000, 143975, 462320328386], 'label': '77760.bo.3240.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.eo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.eo1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056232
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.ez1', '1620.a1', '1620.bt1', '1620.eg1', '1620.fn1', '1620.gl1', '1620.gx1', '1620.ho1'], 'contains': ['6480.cj2', '6480.dc1', '6480.dg1', '9720.bn1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [7185029309, 179012, 19678982400, 462320328485], 'label': '77760.bo.3240.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.ep1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ep1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056233
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.fa1', '1620.b1', '1620.bs1', '1620.eg1', '1620.eq1', '1620.hh1'], 'contains': ['6480.cj2', '6480.dd1', '6480.dh1', '9720.bo1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [7185207845, 462320283121, 19678982400, 143975], 'label': '77760.bo.3240.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.eq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.eq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056234
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.fb1', '1620.b1', '1620.bt1', '1620.ef1', '1620.ex1', '1620.ha1'], 'contains': ['6480.cj2', '6480.df1', '6480.di1', '9720.bp1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [19679063280, 462320225425, 80880, 7185202680], 'label': '77760.bo.3240.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.er1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.er1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056235
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.d2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.fw1', '1080.fc1', '1620.g1', '1620.bv1', '1620.eh1', '1620.er1', '1620.gm1', '1620.gs1', '1620.ho1'], 'contains': ['6480.cj1', '6480.dc1', '9720.br1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [87261753748, 456053074316, 83467916, 148], 'label': '77760.bo.3240.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.es1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.es1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246056236
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.bc1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.et1', '1080.fd1', '1620.bl1', '1620.cf1', '1620.cs2', '1620.et1', '1620.gn1', '1620.gt1', '1620.hk1'], 'contains': ['6480.ck2', '6480.cm1', '6480.cq1', '6480.dz1', '6480.dz2', '9720.bh1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841090505, 19679028004, 462320328958, 80787], 'label': '77760.bo.3240.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.et1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.et1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056256
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.fk1', '1620.l1', '1620.bf1', '1620.eg1', '1620.ew1', '1620.hm1'], 'contains': ['6480.cl2', '6480.dd1', '6480.dg1', '9720.bo1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [19679063280, 462320092205, 7185162389, 80880], 'label': '77760.bo.3240.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.fj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.fj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056237
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.et2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.bc1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.et2', '1080.fd2', '1620.bl2', '1620.cf1', '1620.cs1', '1620.es2', '1620.gu1', '1620.gv1', '1620.hd1'], 'contains': ['6480.ck1', '6480.cm2', '6480.cq1', '6480.dz1', '6480.dz2', '9720.bh2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841223825, 19679028004, 462320230444, 80787], 'label': '77760.bo.3240.et2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.et2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.et2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056238
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.d1', '30.d1', '45.a1'], 'contains': ['180.bj1', '180.bk1', '180.bs1', '180.el1', '180.em1', '180.ey1', '180.fa1', '270.s1', '270.t1', '270.bf1', '360.bl1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841090505, 80787, 262496586387, 85805, 462320328958, 19678982548, 448908283914, 80880], 'label': '77760.bo.90.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '90.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.q1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246056239
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fx1', '1080.eu1', '1080.fe1', '1620.bk1', '1620.bz1', '1620.ct1', '1620.es1', '1620.gt1', '1620.hd1', '1620.hk1'], 'contains': ['6480.ck1', '6480.cm1', '6480.cy1', '9720.bi1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [83548555, 456053150130, 87261834387, 80787], 'label': '77760.bo.3240.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.eu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.eu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056240
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.fd1', '1620.u1', '1620.bj1', '1620.ds2', '1620.ew1', '1620.go1', '1620.gp1', '1620.hl1'], 'contains': ['6480.cl2', '6480.cn1', '6480.cp1', '6480.ec1', '6480.ec2', '9720.bh1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841090505, 179012, 19678982400, 462320363997], 'label': '77760.bo.3240.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.ev1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ev1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056241
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ev2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.fd2', '1620.u1', '1620.bj2', '1620.ds1', '1620.eu1', '1620.gr1', '1620.gw1', '1620.hg1'], 'contains': ['6480.cl1', '6480.cn2', '6480.cp1', '6480.ec1', '6480.ec2', '9720.bh2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [19679063280, 461841188401, 462320149704, 80880], 'label': '77760.bo.3240.ev2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.ev2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ev2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056242
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fy1', '1080.fe1', '1620.o1', '1620.bi1', '1620.dt1', '1620.ev1', '1620.gq1', '1620.hg1', '1620.hl1'], 'contains': ['6480.cl1', '6480.cn1', '6480.de1', '9720.bi1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [87261753748, 456053069398, 148, 83467561], 'label': '77760.bo.3240.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.ew1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ew1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056243
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.ff1', '1620.r1', '1620.bg1', '1620.ee1', '1620.ex1', '1620.ez1', '1620.gw1', '1620.hl1'], 'contains': ['6480.cl1', '6480.cp1', '6480.di1', '9720.bk1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [87182201788, 224515, 375138172555, 482716346], 'label': '77760.bo.3240.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.ex1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ex1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056244
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.cg2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.ev1', '1080.fg1', '1620.bm1', '1620.by1', '1620.dd1', '1620.fb1', '1620.fi1', '1620.gt1', '1620.gu1'], 'contains': ['6480.ck1', '6480.cq1', '6480.cv1', '9720.bj1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [375138172205, 80787, 87182000787, 482670985], 'label': '77760.bo.3240.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.ey1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ey1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056245
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.ew1', '1080.ff1', '1620.bh1', '1620.ce1', '1620.dd1', '1620.fa1', '1620.fc1', '1620.gv1', '1620.hk1'], 'contains': ['6480.ck1', '6480.cq1', '6480.da1', '9720.bk1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [482635561, 375138172555, 80787, 87182000787], 'label': '77760.bo.3240.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.ez1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ez1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056246
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.fg1', '1620.n1', '1620.bn1', '1620.ee1', '1620.fd1', '1620.fj1', '1620.gq1', '1620.gr1'], 'contains': ['6480.cl1', '6480.cr1', '6480.db1', '9720.bj1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [375138172205, 482670749, 80880, 87181920000], 'label': '77760.bo.3240.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.fa1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.fa1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056247
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.ex1', '1080.fh1', '1620.bh1', '1620.by1', '1620.dj1', '1620.es1', '1620.es2', '1620.gy1', '1620.hn1'], 'contains': ['6480.ck1', '6480.cs1', '6480.cz1', '9720.bl1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [482854444, 375138172205, 80787, 87182000787], 'label': '77760.bo.3240.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.fb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.fb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056248
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.fh1', '1620.n1', '1620.bg1', '1620.ej1', '1620.eu1', '1620.ev1', '1620.gx1', '1620.hm1'], 'contains': ['6480.cl1', '6480.ct1', '6480.dg1', '9720.bl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [482854584, 375138172205, 80880, 87181920000], 'label': '77760.bo.3240.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.fc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.fc1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056249
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['30.f1', '45.a1'], 'contains': ['180.d1', '180.j1', '180.ba1', '180.bj1', '180.bu1', '180.cc1', '180.cj1', '270.u1', '270.x1', '270.bj1', '360.bp1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841090505, 80787, 262496586694, 85805, 19678982548, 80880, 462320046985, 693], 'label': '77760.bo.90.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '90.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.r1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246056250
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.dv1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.ey1', '1080.fi1', '1620.bc1', '1620.bw1', '1620.de1', '1620.fi1', '1620.gt1'], 'contains': ['6480.ck2', '6480.cv1', '6480.cy1', '9720.bm1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [7185024000, 19679028004, 462320328958, 80787], 'label': '77760.bo.3240.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.fd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.fd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056251
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.dv1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.ez1', '1080.fj1', '1620.bc1', '1620.bx1', '1620.df1', '1620.fo1', '1620.gn1', '1620.gy1', '1620.hp1'], 'contains': ['6480.ck2', '6480.cw1', '6480.cz1', '9720.bn1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [7185207845, 462320225425, 19679028004, 80787], 'label': '77760.bo.3240.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.fe1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.fe1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056252
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.fa1', '1080.fk1', '1620.bd1', '1620.bw1', '1620.df1', '1620.et1', '1620.hn1'], 'contains': ['6480.ck2', '6480.cx1', '6480.cz1', '9720.bo1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [7185207845, 19679028004, 80787, 462320046985], 'label': '77760.bo.3240.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.ff1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ff1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056253
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.fb1', '1080.fl1', '1620.bd1', '1620.bx1', '1620.de1', '1620.fa1', '1620.hk1'], 'contains': ['6480.ck2', '6480.cy1', '6480.da1', '9720.bp1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [462320225425, 19679028004, 80787, 7185202680], 'label': '77760.bo.3240.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.fg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.fg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056254
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.fi1', '1620.l1', '1620.be1', '1620.ef1', '1620.fj1', '1620.gp1'], 'contains': ['6480.cl2', '6480.db1', '6480.df1', '9720.bm1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [19679063280, 7185104880, 80880, 462320046985], 'label': '77760.bo.3240.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.fh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.fh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056255
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.fj1', '1620.m1', '1620.be1', '1620.eg1', '1620.fp1', '1620.go1', '1620.gs1', '1620.hq1'], 'contains': ['6480.cl2', '6480.dc1', '6480.dh1', '9720.bn1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [19679063280, 462320092205, 7185029309, 80880], 'label': '77760.bo.3240.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.fi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.fi1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056257
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.fl1', '1620.m1', '1620.bf1', '1620.ef1', '1620.ey1', '1620.hl1'], 'contains': ['6480.cl2', '6480.de1', '6480.di1', '9720.bp1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [179012, 19678982400, 462320328958, 7185202680], 'label': '77760.bo.3240.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.fk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.fk1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056258
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.fm1', '1620.e1', '1620.bj2', '1620.ek1', '1620.ex1', '1620.gq1', '1620.gx1', '1620.hh1'], 'contains': ['6480.cj2', '6480.cl1', '6480.ct1', '6480.ed1', '6480.ed2', '9720.bq1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [19679063280, 461841183480, 462320225425, 80880], 'label': '77760.bo.3240.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.fl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.fl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056259
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.fl2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.fm2', '1620.e2', '1620.bj1', '1620.ek1', '1620.ey1', '1620.gp1', '1620.gs1', '1620.hm1'], 'contains': ['6480.cj1', '6480.cl2', '6480.ct1', '6480.ed1', '6480.ed2', '9720.bq1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [179012, 461841183480, 19678982400, 462320328958], 'label': '77760.bo.3240.fl2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.fl2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.fl2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056260
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.i1', '30.g1', '45.a1'], 'contains': ['180.e1', '180.k1', '180.bd1', '180.bk1', '180.bu1', '180.ce1', '180.ck1', '270.v1', '270.y1', '270.bh1', '360.bq1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [80787, 482768881, 143304, 87182058242, 85805, 375138172205, 188331315147, 80880], 'label': '77760.bo.90.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '90.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.s1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246056261
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['360.fz1', '1080.fn1', '1620.d1', '1620.bi1', '1620.eh1', '1620.ez1', '1620.gr1', '1620.hh1', '1620.hm1'], 'contains': ['6480.cj1', '6480.cl1', '6480.dd1', '9720.bs1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [456053207518, 83548555, 87262035388, 224515], 'label': '77760.bo.3240.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.fm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.fm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056262
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.bc1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.fm1', '1080.fm2', '1620.bl1', '1620.bl2', '1620.dm1', '1620.fa1', '1620.gt1', '1620.gy1', '1620.hn1'], 'contains': ['6480.ck1', '6480.ck2', '6480.cs1', '6480.eg1', '6480.eg2', '9720.bq1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [462320225425, 19679028004, 461841148348, 80787], 'label': '77760.bo.3240.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.fn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.fn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056263
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.cg2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.ga1', '1080.fc1', '1080.fo1', '1620.bo1', '1620.bz1', '1620.dg1', '1620.fb1', '1620.gv1', '1620.gy1', '1620.hp1'], 'contains': ['6480.ck1', '6480.cw1', '9720.br1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [83548555, 456053154955, 87261834387, 80787], 'label': '77760.bo.3240.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.fo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.fo1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056264
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.gb1', '1080.fn1', '1620.bk1', '1620.dg1', '1620.fc1', '1620.gu1', '1620.hn1'], 'contains': ['6480.ck1', '6480.cx1', '9720.bs1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [83548555, 456053073961, 87261834387, 80787], 'label': '77760.bo.3240.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.fp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.fp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056265
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.gc1', '1080.fo1', '1620.o1', '1620.bp1', '1620.eh1', '1620.fd1', '1620.gw1', '1620.gx1', '1620.hq1'], 'contains': ['6480.cl1', '6480.dc1', '9720.br1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [83548555, 87262035388, 456053154955, 224515], 'label': '77760.bo.3240.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.fq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.fq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056266
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.fp1', '1080.fq1', '1620.by1', '1620.ce1', '1620.cu1', '1620.es1', '1620.et1', '1620.gn1', '1620.hd1'], 'contains': ['6480.cm1', '6480.cq1', '6480.cz1', '9720.bt1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [375138087093, 80787, 87182000787, 482670985], 'label': '77760.bo.3240.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.fr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.fr1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056267
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bs2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.fr1', '1080.fs1', '1620.by1', '1620.cx1', '1620.fe1', '1620.fk1', '1620.gt1'], 'contains': ['6480.cm1', '6480.cs1', '6480.cv1', '9720.bu1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [375138087093, 80787, 87182000787, 482676354], 'label': '77760.bo.3240.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.fs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.fs1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246056268
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.cv1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.ft1', '1080.fx1', '1620.bw1', '1620.cv1', '1620.fk1', '1620.gu1'], 'contains': ['6480.cm2', '6480.cv1', '6480.cx1', '9720.bv1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [462320323891, 7185024000, 19679028004, 80787], 'label': '77760.bo.3240.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.ft1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ft1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056269
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.cv1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.fu1', '1080.fy1', '1620.bx1', '1620.cv1', '1620.fq1', '1620.gv1', '1620.hr1'], 'contains': ['6480.cm2', '6480.cw1', '6480.da1', '9720.bw1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [19679028004, 80787, 7185202680, 462320230347], 'label': '77760.bo.3240.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.fu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.fu1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056270
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.fv1', '1080.fw1', '1620.bw1', '1620.bx1', '1620.cw1', '1620.es2', '1620.hd1'], 'contains': ['6480.cm2', '6480.cy1', '6480.cz1', '9720.bx1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [7185029309, 462320323652, 19679028004, 80787], 'label': '77760.bo.3240.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.fv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.fv1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056271
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.e1', '30.h1', '45.a1'], 'contains': ['180.l1', '180.o1', '180.bo1', '180.bs1', '180.bu1', '180.cl1', '180.cn1', '270.w1', '270.z1', '270.bk1', '360.br1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [374659361758, 87182277597, 362615, 262972155450, 355938110909, 85805, 80880, 80787], 'label': '77760.bo.90.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '90.t1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.t1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246056272
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bs2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.gd1', '1080.fz1', '1080.ga1', '1620.bz1', '1620.cy1', '1620.fe1', '1620.gn1', '1620.hr1'], 'contains': ['6480.cm1', '6480.cw1', '9720.by1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [83543730, 456053150130, 87261834387, 80787], 'label': '77760.bo.3240.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.fw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.fw1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246056273
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.fp1', '1620.r1', '1620.bu1', '1620.du1', '1620.eo1', '1620.eq1', '1620.go1', '1620.hg1'], 'contains': ['6480.cn1', '6480.cp1', '6480.dh1', '9720.bt1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [482635916, 375138087093, 148, 87181920000], 'label': '77760.bo.3240.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.fx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.fx1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056274
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.fq1', '1620.n1', '1620.cc1', '1620.du1', '1620.ev1', '1620.ew1', '1620.gl1', '1620.gz1'], 'contains': ['6480.cn1', '6480.cr1', '6480.dg1', '9720.bt1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [482849425, 375138087093, 143975, 87182282187], 'label': '77760.bo.3240.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.fy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.fy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056275
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.v2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.fr1', '1620.n1', '1620.bu1', '1620.dy1', '1620.ff1', '1620.fl1', '1620.gp1', '1620.gq1'], 'contains': ['6480.cn1', '6480.ct1', '6480.db1', '9720.bu1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [179012, 443120204612, 180667244280, 442641341252], 'label': '77760.bo.3240.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.fz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.fz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056276
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.fs1', '1620.dz1', '1620.fg1', '1620.fm1'], 'contains': ['6480.co1', '6480.cu1', '6480.dj1', '9720.bu1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [443120250212, 180667289784, 442641341252, 224612], 'label': '77760.bo.3240.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '3240.ga1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ga1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056277
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.ft1', '1620.l1', '1620.bs1', '1620.dv1', '1620.fl1', '1620.gr1'], 'contains': ['6480.cn2', '6480.db1', '6480.dd1', '9720.bv1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [19678982400, 7185024000, 143975, 462320369015], 'label': '77760.bo.3240.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.gb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.gb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056278
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.fu1', '1620.m1', '1620.bt1', '1620.dv1', '1620.fr1', '1620.gm1', '1620.gw1', '1620.hs1'], 'contains': ['6480.cn2', '6480.dc1', '6480.di1', '9720.bw1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [179012, 462320323652, 19678982400, 7185202680], 'label': '77760.bo.3240.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.gc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.gc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056279
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.fv1', '1620.m1', '1620.bs1', '1620.dw1', '1620.ep1', '1620.hg1'], 'contains': ['6480.cn2', '6480.de1', '6480.dh1', '9720.bx1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [7185029309, 45363, 19679027763, 462320369015], 'label': '77760.bo.3240.gd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.gd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.gd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056280
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.fw1', '1620.l1', '1620.bt1', '1620.dw1', '1620.eu1', '1620.gz1'], 'contains': ['6480.cn2', '6480.df1', '6480.dg1', '9720.bx1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [7185029309, 179012, 462320323652, 19678982400], 'label': '77760.bo.3240.ge1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.ge1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ge1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056281
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.fx1', '1620.dx1', '1620.fm1'], 'contains': ['6480.co2', '6480.dj1', '6480.dl1', '9720.bv1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [19678982400, 7185024000, 462320369015, 179159], 'label': '77760.bo.3240.gf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '3240.gf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.gf1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056282
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3.a1'], 'contains': ['18.a1', '18.b1', '18.d1', '18.e1', '18.g1', '18.l1', '18.n1', '27.a1', '54.d1', '90.e1', '135.a1'], 'core': '108.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [5066, 148, 93924236159, 462320011466, 693], 'label': '77760.bo.9.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '9.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
  • id: 246056283
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['45.b1'], 'contains': ['180.t1', '180.u1', '180.be1', '180.bf1', '180.bv2', '180.bw1', '180.bx1', '180.cs1', '180.ct1', '180.cy1', '180.cz1', '270.bg1'], 'core': '720.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [143975, 80787, 7185162389, 143304, 85805, 19678982548, 80880, 462320328386], 'label': '77760.bo.90.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '90.u1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.u1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246056284
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.fy1', '1620.dx1', '1620.fs1', '1620.ht1'], 'contains': ['6480.co2', '6480.dk1', '6480.dm1', '9720.bw1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [19678982400, 7185202680, 462320369015, 179159], 'label': '77760.bo.3240.gg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '3240.gg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.gg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056285
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.v2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['360.ge1', '1080.fz1', '1620.o1', '1620.bv1', '1620.ea1', '1620.ff1', '1620.gl1', '1620.go1', '1620.hs1'], 'contains': ['6480.cn1', '6480.dc1', '9720.by1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [87261753748, 456053069398, 83462998, 148], 'label': '77760.bo.3240.gh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.gh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.gh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056286
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.gf1', '1080.ga1', '1620.eb1', '1620.fg1', '1620.ht1'], 'contains': ['6480.co1', '6480.dk1', '9720.by1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [87262115884, 456053069398, 83462998, 179159], 'label': '77760.bo.3240.gi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '3240.gi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.gi1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056287
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.gb1', '1620.v1', '1620.ca1', '1620.el1', '1620.eo1', '1620.eu1', '1620.ex1', '1620.gp1'], 'contains': ['6480.cp1', '6480.ct1', '6480.df1', '9720.bz1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [87182277125, 355938248904, 143975, 374659446987], 'label': '77760.bo.3240.gj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.gj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.gj1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056288
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.d2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.gc1', '1620.y1', '1620.ca1', '1620.ei1', '1620.er1', '1620.fn1', '1620.go1', '1620.gw1'], 'contains': ['6480.cp1', '6480.dc1', '9720.ca1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [374659130163, 355938382558, 87182277597, 45363], 'label': '77760.bo.3240.gk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.gk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.gk1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246056289
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.gb1', '1080.gd1', '1620.cb1', '1620.ch1', '1620.dn1', '1620.es1', '1620.es2', '1620.fa1', '1620.gt1'], 'contains': ['6480.cq1', '6480.cs1', '6480.cy1', '9720.bz1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [87181925066, 374659084800, 355938248904, 80787], 'label': '77760.bo.3240.gl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.gl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.gl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056290
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.gd1', '1620.p1', '1620.cg1', '1620.el1', '1620.ep1', '1620.ev1', '1620.ey1', '1620.gq1'], 'contains': ['6480.cr1', '6480.ct1', '6480.de1', '9720.bz1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [374659165680, 355938284280, 87181925066, 80880], 'label': '77760.bo.3240.gm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.gm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.gm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056291
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.ge1', '1620.v1', '1620.cg1', '1620.ei1', '1620.eq1', '1620.ew1', '1620.ez1', '1620.gr1'], 'contains': ['6480.cp1', '6480.cr1', '6480.dd1', '9720.cb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [355938243842, 87182277125, 143975, 374659446987], 'label': '77760.bo.3240.gn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.gn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.gn1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056292
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.cg2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.gc1', '1080.gf1', '1620.cb1', '1620.ci1', '1620.dh1', '1620.fb1', '1620.fo1', '1620.gn1', '1620.gv1'], 'contains': ['6480.cq1', '6480.cw1', '9720.ca1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [87182277597, 374659084800, 355938382650, 80787], 'label': '77760.bo.3240.go1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.go1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.go1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056293
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.ge1', '1620.ch1', '1620.dh1', '1620.et1', '1620.fc1', '1620.gu1'], 'contains': ['6480.cq1', '6480.cx1', '9720.cb1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [355938289445, 87181925066, 374659084800, 80787], 'label': '77760.bo.3240.gp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.gp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.gp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056294
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['30.g1', '45.b1'], 'contains': ['180.v1', '180.y1', '180.bg1', '180.bm1', '180.bv1', '180.bw1', '180.by1', '180.cr1', '180.cu1', '180.cx1', '180.dc1', '270.bh1'], 'core': '720.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [87182277597, 143975, 375138270474, 482768881, 85805, 80880, 80787, 143304], 'label': '77760.bo.90.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '90.v1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.v1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246056295
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.gf1', '1620.p1', '1620.cj1', '1620.ei1', '1620.fd1', '1620.fp1', '1620.gl1', '1620.gm1'], 'contains': ['6480.cr1', '6480.dc1', '9720.ca1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [355938243842, 87182277597, 143975, 374659446987], 'label': '77760.bo.3240.gq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.gq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.gq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056296
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bs2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.gg1', '1080.gh1', '1620.cb1', '1620.dq1', '1620.fe1', '1620.fq1', '1620.gy1'], 'contains': ['6480.cs1', '6480.cw1', '9720.cc1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [374659084800, 87182202116, 355938468215, 80787], 'label': '77760.bo.3240.gr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.gr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.gr1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246056297
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.gs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.v2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.gg1', '1620.p1', '1620.ca1', '1620.em1', '1620.ff1', '1620.fr1', '1620.gs1', '1620.gx1'], 'contains': ['6480.ct1', '6480.dc1', '9720.cc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [355938248904, 143975, 374659446987, 87182282615], 'label': '77760.bo.3240.gs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.gs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.gs1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056298
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.gt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.gh1', '1620.en1', '1620.fg1', '1620.fs1'], 'contains': ['6480.cu1', '6480.dk1', '9720.cc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [355938284280, 374659447084, 87182282615, 179159], 'label': '77760.bo.3240.gt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '3240.gt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.gt1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056299
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.gu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.d2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.gj1', '1080.gk1', '1080.gl1', '1620.f1', '1620.cc1', '1620.ej1', '1620.ft1', '1620.gz1', '1620.hm1', '1620.ho1'], 'contains': ['6480.cj1', '6480.dg1', '6480.dq1', '9720.cd1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [148, 375138172555, 87181920000, 482630643], 'label': '77760.bo.3240.gu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.gu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.gu1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246056300
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.gv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.gi1', '1080.gm1', '1620.h1', '1620.cd1', '1620.ek1', '1620.fh1', '1620.ha1', '1620.hh1', '1620.ho1'], 'contains': ['6480.cj1', '6480.cj2', '6480.dq1', '9720.ce1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841050163, 45363, 462320328958, 19679027763], 'label': '77760.bo.3240.gv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '3240.gv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.gv1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056301
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.gw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.gi1', '1080.gn1', '1080.gp1', '1620.i1', '1620.q1', '1620.di1', '1620.gf1', '1620.hb1', '1620.hi1', '1620.hu1'], 'contains': ['6480.ds1', '9720.ce1', '12960.x1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [355462732800, 375138126985, 87660962185, 462320046985], 'label': '77760.bo.3240.gw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '3240.gw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.gw1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056302
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.gx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.gi1', '1080.go1', '1620.j1', '1620.hc1', '1620.hj1'], 'contains': ['6480.du1', '9720.ce1', '12960.y1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [461841004800, 19678982400, 262496550963, 462320328958], 'label': '77760.bo.3240.gx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1', 'old_label': '3240.gx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.gx1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056303
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.gy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.cg2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.gj1', '1080.gq1', '1080.gr1', '1080.gs1', '1620.bm1', '1620.ce1', '1620.dj1', '1620.fu1', '1620.hd1', '1620.hn1', '1620.hp1'], 'contains': ['6480.ck1', '6480.cz1', '6480.dp1', '9720.cd1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [482676004, 375138172205, 80787, 87182000787], 'label': '77760.bo.3240.gy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.gy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.gy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056304
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.gz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.gq1', '1080.gt1', '1080.gu1', '1620.r1', '1620.bn1', '1620.ej1', '1620.fv1', '1620.hg1', '1620.hh1', '1620.hq1'], 'contains': ['6480.cl1', '6480.dh1', '6480.dq1', '9720.cd1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [482630400, 143975, 375138172555, 87182282187], 'label': '77760.bo.3240.gz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.gz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.gz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056305
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1', '45.b1'], 'contains': ['180.w1', '180.z1', '180.bh1', '180.bv1', '180.bx1', '180.cq1', '180.cv1', '180.da1', '270.bi1'], 'core': '720.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [456053074316, 87262035243, 83543730, 143975, 85805, 80880, 80787, 143304], 'label': '77760.bo.90.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '90.w1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.w1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246056306
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ha1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.q1', '1080.gk1', '1080.gr1', '1080.gt1', '1620.k1', '1620.s1', '1620.dk1', '1620.fw1', '1620.he1', '1620.hi1', '1620.hu1'], 'contains': ['6480.ds1', '9720.cd1', '12960.bb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [482630400, 188331091200, 375138172205, 87181920000], 'label': '77760.bo.3240.ha1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '3240.ha1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ha1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056307
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.hb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.gl1', '1080.gr1', '1080.gu1', '1620.dl1', '1620.fx1', '1620.hf1'], 'contains': ['6480.dt1', '9720.cd1', '12960.bc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [443120025600, 442641301050, 442162103187, 180667065600], 'label': '77760.bo.3240.hb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bu1', 'old_label': '3240.hb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.hb1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056308
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.hc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.gs1', '1080.gt1', '1080.gu1', '1620.t1', '1620.fy1', '1620.hj1'], 'contains': ['6480.du1', '9720.cd1', '12960.bd1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [443120025600, 442641301050, 442162166375, 180667065600], 'label': '77760.bo.3240.hc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.f1', 'old_label': '3240.hc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.hc1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056309
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.hd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.ec1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.gm1', '1080.gn1', '1080.go1', '1080.gv1', '1620.bq1', '1620.cf1', '1620.dm1', '1620.fi1', '1620.hk1', '1620.hn1', '1620.hp1'], 'contains': ['6480.ck1', '6480.ck2', '6480.dp1', '9720.ce1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [19679028004, 461841050404, 462320328958, 80787], 'label': '77760.bo.3240.hd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '3240.hd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.hd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056310
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.he1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.gp1', '1080.gv1', '1620.u1', '1620.br1', '1620.ek1', '1620.fj1', '1620.hl1', '1620.hm1', '1620.hq1'], 'contains': ['6480.cl1', '6480.cl2', '6480.dq1', '9720.ce1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841004800, 19678982400, 143975, 462320328958], 'label': '77760.bo.3240.he1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '3240.he1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.he1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056311
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.hf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bs2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.gx1', '1080.gy1', '1080.gz1', '1080.ha1', '1080.hb1', '1620.ce1', '1620.cx1', '1620.fz1', '1620.hk1', '1620.hr1'], 'contains': ['6480.cm1', '6480.da1', '6480.dp1', '9720.cf1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [482676004, 375138087093, 80787, 87182000787], 'label': '77760.bo.3240.hf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.hf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.hf1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246056312
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.hg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.cz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.gw1', '1080.hc1', '1080.hd1', '1620.cf1', '1620.cz1', '1620.fk1', '1620.hd1', '1620.hr1'], 'contains': ['6480.cm1', '6480.cm2', '6480.dp1', '9720.cg1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [448908278999, 462320323799, 19679028004, 80787], 'label': '77760.bo.3240.hg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '3240.hg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.hg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056313
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.hh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.gw1', '1080.he1', '1080.hg1', '1620.q1', '1620.da1', '1620.gg1', '1620.he1', '1620.hv1'], 'contains': ['6480.ds1', '9720.cg1', '12960.bf1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [355462732800, 87661284215, 375138449015, 462320369015], 'label': '77760.bo.3240.hh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '3240.hh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.hh1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056314
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.hi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.gw1', '1080.hf1', '1080.hh1', '1620.db1', '1620.hf1'], 'contains': ['6480.dt1', '9720.cg1', '12960.bg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841004800, 19678982400, 262496586387, 462320369015], 'label': '77760.bo.3240.hi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bl1', 'old_label': '3240.hi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.hi1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056315
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.hj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.v2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.gx1', '1080.hi1', '1620.r1', '1620.cc1', '1620.dy1', '1620.ga1', '1620.ha1', '1620.hl1', '1620.hs1'], 'contains': ['6480.cn1', '6480.di1', '6480.dq1', '9720.cf1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [375138087093, 482630400, 143975, 87182282187], 'label': '77760.bo.3240.hj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.hj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.hj1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056316
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['30.f1', '45.b1'], 'contains': ['180.x1', '180.x2', '180.bc1', '180.bn1', '180.bv1', '180.bv2', '180.by1', '180.cp1', '180.cp2', '180.cw1', '180.dd1', '270.bj1'], 'core': '720.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [143975, 80787, 143304, 85805, 19678982548, 448908283914, 80880, 462320328386], 'label': '77760.bo.90.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '90.x1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.x1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246056317
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.hk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.gy1', '1080.hj1', '1620.dz1', '1620.gb1', '1620.ht1'], 'contains': ['6480.co1', '6480.dm1', '6480.dr1', '9720.cf1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87182237067, 375138087093, 482630400, 224612], 'label': '77760.bo.3240.hk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '3240.hk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.hk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056318
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.hl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.r1', '1080.gz1', '1080.hi1', '1080.hj1', '1620.s1', '1620.dc1', '1620.gc1', '1620.hb1', '1620.hv1'], 'contains': ['6480.ds1', '9720.cf1', '12960.bj1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [375138087093, 482630400, 188331091200, 87181920000], 'label': '77760.bo.3240.hl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '3240.hl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.hl1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056319
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.hm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.ha1', '1080.hi1', '1620.t1', '1620.gd1', '1620.hc1'], 'contains': ['6480.du1', '9720.cf1', '12960.bk1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [375138087093, 482630400, 188331091348, 87181920000], 'label': '77760.bo.3240.hm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.l1', 'old_label': '3240.hm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.hm1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056320
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.hn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.hb1', '1080.hj1', '1620.ge1'], 'contains': ['6480.dv1', '9720.cf1', '12960.bl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [443120025600, 442162247012, 442641341252, 180667065600], 'label': '77760.bo.3240.hn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.fp1', 'old_label': '3240.hn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.hn1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056321
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ho1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.bq1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.hc1', '1080.he1', '1080.hf1', '1620.u1', '1620.cd1', '1620.ec1', '1620.fl1', '1620.gz1', '1620.hg1', '1620.hs1'], 'contains': ['6480.cn1', '6480.cn2', '6480.dq1', '9720.cg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [462320288371, 19678982400, 224515, 448908243571], 'label': '77760.bo.3240.ho1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '3240.ho1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ho1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056322
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.hp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.hd1', '1080.hg1', '1080.hh1', '1620.ed1', '1620.fm1', '1620.ht1'], 'contains': ['6480.co1', '6480.co2', '6480.dr1', '9720.cg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841004800, 19678982400, 462320369015, 179159], 'label': '77760.bo.3240.hp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '3240.hp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.hp1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056323
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.hq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.d2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.hk1', '1080.hl1', '1080.hm1', '1620.y1', '1620.cg1', '1620.el1', '1620.fh1', '1620.ft1', '1620.hg1', '1620.hl1'], 'contains': ['6480.cp1', '6480.de1', '6480.dq1', '9720.ch1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [374659130163, 87182277597, 355938150963, 45363], 'label': '77760.bo.3240.hq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.hq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.hq1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246056324
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.hr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.cg2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.hk1', '1080.hn1', '1080.ho1', '1080.hp1', '1620.ch1', '1620.ci1', '1620.dn1', '1620.fi1', '1620.fu1', '1620.hd1', '1620.hk1'], 'contains': ['6480.cq1', '6480.cy1', '6480.dp1', '9720.ch1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87182277597, 374659084800, 355938105600, 80787], 'label': '77760.bo.3240.hr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.hr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.hr1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056325
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.hs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.hn1', '1080.hq1', '1080.hr1', '1620.v1', '1620.cj1', '1620.el1', '1620.fj1', '1620.fv1', '1620.gz1', '1620.ha1'], 'contains': ['6480.cr1', '6480.df1', '6480.dq1', '9720.ch1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [374659165680, 87181925066, 355938186480, 80880], 'label': '77760.bo.3240.hs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '3240.hs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.hs1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056326
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ht1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.hl1', '1080.ho1', '1080.hq1', '1620.w1', '1620.z1', '1620.do1', '1620.fw1', '1620.gf1', '1620.hb1', '1620.he1'], 'contains': ['6480.ds1', '9720.ch1', '12960.bp1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87182277597, 374659084800, 355938105600, 262971878400], 'label': '77760.bo.3240.ht1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '3240.ht1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ht1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056327
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.h1', '45.b1'], 'contains': ['180.bi1', '180.bq1', '180.br1', '180.bx1', '180.by1', '180.db1', '180.de1', '180.df1', '270.bk1'], 'core': '720.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [374659361758, 87182277597, 143975, 355938110909, 85805, 80880, 80787, 143304], 'label': '77760.bo.90.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '90.y1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.y1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246056328
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.hu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.hm1', '1080.ho1', '1080.hr1', '1620.dp1', '1620.fx1', '1620.hf1'], 'contains': ['6480.dt1', '9720.ch1', '12960.bq1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [87181925066, 374659084800, 355938105600, 262971959187], 'label': '77760.bo.3240.hu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bu1', 'old_label': '3240.hu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.hu1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056329
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.hv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.hp1', '1080.hq1', '1080.hr1', '1620.x1', '1620.fy1', '1620.hc1'], 'contains': ['6480.du1', '9720.ch1', '12960.br1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [87181925066, 262971878548, 374659084800, 355938105600], 'label': '77760.bo.3240.hv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.f1', 'old_label': '3240.hv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.hv1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056330
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.hw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bs2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.hs1', '1080.ht1', '1080.hu1', '1080.hv1', '1080.hw1', '1620.ch1', '1620.dq1', '1620.fk1', '1620.fz1', '1620.hn1'], 'contains': ['6480.cs1', '6480.cx1', '6480.dp1', '9720.ci1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [374659084800, 355938105600, 87182202116, 80787], 'label': '77760.bo.3240.hw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '3240.hw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.hw1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246056331
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.hx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.v2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.hs1', '1080.hx1', '1620.v1', '1620.cg1', '1620.em1', '1620.fl1', '1620.ga1', '1620.hh1', '1620.hm1'], 'contains': ['6480.ct1', '6480.dd1', '6480.dq1', '9720.ci1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [355938105600, 143975, 374659446987, 87182282615], 'label': '77760.bo.3240.hx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.hx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.hx1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056332
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.hy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.ht1', '1080.hy1', '1620.en1', '1620.fm1', '1620.gb1'], 'contains': ['6480.cu1', '6480.dl1', '6480.dr1', '9720.ci1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [374659447084, 355938105600, 87182282615, 179159], 'label': '77760.bo.3240.hy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '3240.hy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.hy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246056333
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.hz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.hu1', '1080.hx1', '1080.hy1', '1620.w1', '1620.dr1', '1620.gc1', '1620.gg1', '1620.hi1'], 'contains': ['6480.ds1', '9720.ci1', '12960.bv1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [374659084800, 355938105600, 262971878400, 87182282615], 'label': '77760.bo.3240.hz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '3240.hz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.hz1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056334
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ia1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.hv1', '1080.hx1', '1620.x1', '1620.gd1', '1620.hj1'], 'contains': ['6480.du1', '9720.ci1', '12960.bw1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [374659084800, 19203891388, 87657516984, 87181920000], 'label': '77760.bo.3240.ia1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.l1', 'old_label': '3240.ia1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ia1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056335
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ib1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.hw1', '1080.hy1', '1620.ge1'], 'contains': ['6480.dv1', '9720.ci1', '12960.bx1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [374659084800, 355938105600, 262972240824, 87182282615], 'label': '77760.bo.3240.ib1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.fp1', 'old_label': '3240.ib1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ib1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056336
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ic1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.cp2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.hz1', '1080.ia1', '1080.if1', '1620.ci1', '1620.dq1', '1620.gh1', '1620.hp1', '1620.hr1'], 'contains': ['6480.cw1', '6480.dp1', '9720.cj1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [374659084800, 355938105600, 80787, 87182000787], 'label': '77760.bo.3240.ic1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '3240.ic1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ic1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246056337
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.id1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.r2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.hz1', '1080.ig1', '1620.y1', '1620.cj1', '1620.em1', '1620.gi1', '1620.ho1', '1620.hq1', '1620.hs1'], 'contains': ['6480.dc1', '6480.dq1', '9720.cj1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [374659165680, 355938186480, 80880, 87181920000], 'label': '77760.bo.3240.id1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '3240.id1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.id1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246056338
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['30.i1', '45.a1'], 'contains': ['180.cc1', '180.ck1', '180.cl1', '180.dq1', '180.dt1', '180.em1', '180.er1', '270.bl1', '270.bs1', '270.bt1', '270.bu1', '360.bz1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [362615, 461841004948, 262496787716, 462320052004, 19678982548, 80880, 80787, 448908283914], 'label': '77760.bo.90.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '90.z1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.z1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246056339
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.ie1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.dk2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.ia1', '1080.ih1', '1620.en1', '1620.gj1', '1620.ht1'], 'contains': ['6480.dk1', '6480.dr1', '9720.cj1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [87182282284, 374659447084, 355938105600, 179159], 'label': '77760.bo.3240.ie1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '3240.ie1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.ie1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 246056340
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3240.if1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.bs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.a1', '1080.if1', '1080.ig1', '1080.ih1', '1620.z1', '1620.dr1', '1620.gk1', '1620.hu1', '1620.hv1'], 'contains': ['6480.ds1', '9720.cj1', '12960.v1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [374659084800, 355938105600, 262971878400, 87181920000], 'label': '77760.bo.3240.if1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '3240.if1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.if1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056341
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3888.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.c1', '1296.a1', '1296.c1', '1296.d1', '1944.a1', '1944.b1', '1944.c1'], 'contains': ['7776.a1', '7776.c1', '7776.d1', '19440.b1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [138242, 1037836800, 18764663042], 'label': '77760.bo.3888.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d1', 'old_label': '3888.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 246056342
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3888.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.b1', '1296.e1', '1296.f1', '1944.c1'], 'contains': ['7776.a1', '7776.d1', '7776.e1', '19440.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [1037980104, 138242, 18764663042], 'label': '77760.bo.3888.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.a1', 'old_label': '3888.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 246056343
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3888.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.g1', '1296.h1', '1944.c1'], 'contains': ['7776.a1', '7776.b1', '19440.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [5066, 18764663042, 143304], 'label': '77760.bo.3888.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.a1', 'old_label': '3888.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.c1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 246056344
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3888.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.l1', '1296.i1', '1296.k1', '1296.l1', '1944.c1', '1944.d1', '1944.e1'], 'contains': ['7776.b1', '7776.c1', '7776.e1', '19440.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1037980104, 18764668104, 143304], 'label': '77760.bo.3888.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.e1', 'old_label': '3888.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.d1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 246056345
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3888.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.j1', '1296.m1', '1944.c1'], 'contains': ['7776.b1', '7776.d1', '19440.i1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [178680, 18764703480, 1038020645], 'label': '77760.bo.3888.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.a1', 'old_label': '3888.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.e1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 246056346
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3888.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.p1', '1296.n1', '1296.q1', '1296.u1', '1944.a1', '1944.d1'], 'contains': ['7776.c1', '19440.q1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [181146067200, 269202528000, 267841728000], 'label': '77760.bo.3888.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '3888.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.f1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 246056347
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3888.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.q1', '1296.o1', '1296.r1', '1296.s1', '1944.a1', '1944.b1', '1944.e1'], 'contains': ['7776.c1', '19440.u1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [181146153005, 269202528000, 267841728000], 'label': '77760.bo.3888.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d1', 'old_label': '3888.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.g1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 246056348
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3888.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.r1', '1296.p1', '1296.t1', '1296.v1', '1944.b1', '1944.d1'], 'contains': ['7776.c1', '19440.v1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [181146067893, 269202528000, 267841728000], 'label': '77760.bo.3888.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.e1', 'old_label': '3888.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.h1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 246056349
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['30.j1', '45.a1'], 'contains': ['180.ce1', '180.cj1', '180.cl1', '180.dz1', '180.ea1', '180.el1', '180.eo1', '270.bm1', '270.bq1', '270.bv1', '360.ca1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [448908278999, 262496551413, 224184, 19679028004, 143975, 461841050404, 80787, 462320328241], 'label': '77760.bo.90.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '90.ba1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.ba1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246056350
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.a1', 'complements': ['18.d1', '18.n1', '18.l1', '18.m1', '18.e1'], 'conjugacy_class_count': 2, 'contained_in': ['864.b1', '1440.a1', '1440.h1', '1440.i1', '2160.bj1', '2160.bk1', '2160.bl1', '2160.bm1', '2160.bn1'], 'contains': ['8640.a1', '12960.d1', '12960.e1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [183845, 143975, 80787], 'label': '77760.bo.4320.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4320.a1', 'normal_contained_in': ['12.a1', '1440.a1'], 'normal_contains': ['8640.a1'], 'normalizer': '1.a1', 'old_label': '4320.a1', 'projective_image': '77760.bo', 'quotient_action_image': '6.1', 'quotient_action_kernel': '720.763', 'quotient_action_kernel_order': 720, 'quotient_fusion': None, 'short_label': '4320.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246056351
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.h1', '1440.c1', '1440.d1', '2160.a1', '2160.b1', '2160.e1', '2160.g1', '2160.j1', '2160.k1', '2160.bh1'], 'contains': ['8640.f1', '12960.a1', '12960.b1', '12960.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [183845, 80880, 194518240704], 'label': '77760.bo.4320.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '4320.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056352
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1440.c1', '1440.e1', '2160.c1', '2160.h1', '2160.l1'], 'contains': ['8640.k1', '12960.b1', '12960.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [183845, 193999357680, 280259700485], 'label': '77760.bo.4320.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.a1', 'old_label': '4320.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056353
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1440.c1', '1440.f1', '1440.g1', '2160.d1', '2160.f1', '2160.i1', '2160.m1', '2160.n1'], 'contains': ['8640.m1', '12960.b1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [40349, 280259521949, 193999276800], 'label': '77760.bo.4320.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '4320.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.d1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 246056354
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.a1', '1440.a1', '1440.d1', '2160.o1', '2160.u1', '2160.ba1', '2160.be1', '2160.bn1'], 'contains': ['8640.a1', '12960.a1', '12960.d1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [183845, 80880, 80787], 'label': '77760.bo.4320.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1440.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '4320.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.e1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056355
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.bv1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.bf1', '1440.d1', '1440.e1', '1440.f1', '1440.h1', '2160.p1', '2160.s1', '2160.v1', '2160.y1', '2160.bb1', '2160.bf1', '2160.bi1'], 'contains': ['8640.c1', '12960.b1', '12960.d1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [183845, 355419232804, 80787], 'label': '77760.bo.4320.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '4320.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.f1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056356
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.bb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.bg1', '1440.d1', '1440.e1', '1440.i1', '2160.q1', '2160.bc1', '2160.bg1'], 'contains': ['8640.d1', '12960.c1', '12960.d1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [355419504120, 85805, 80787], 'label': '77760.bo.4320.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1', 'old_label': '4320.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.g1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056357
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.bh1', '1440.g1', '1440.h1', '2160.r1', '2160.t1', '2160.w1', '2160.x1', '2160.z1', '2160.bd1', '2160.bh1'], 'contains': ['8640.f1', '12960.b1', '12960.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [183845, 143975, 194518339175], 'label': '77760.bo.4320.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '4320.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.h1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056358
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.bm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.cg1', '1440.j1', '1440.k1', '1440.l1', '2160.bi1', '2160.bo1', '2160.bp1', '2160.bs1', '2160.bu1', '2160.bx1', '2160.by1'], 'contains': ['8640.c1', '12960.f1', '12960.g1', '12960.h1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [194518195200, 80787, 143304], 'label': '77760.bo.4320.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.r1', 'old_label': '4320.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.i1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056359
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1440.j1', '1440.m1', '1440.o1', '2160.bq1', '2160.bv1', '2160.bz1'], 'contains': ['8640.j1', '12960.g1', '12960.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [193999357894, 280259562387, 693], 'label': '77760.bo.4320.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.bu1', 'old_label': '4320.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.j1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056360
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.g1', '30.k1', '45.a1'], 'contains': ['180.cc1', '180.ce1', '180.cn1', '180.du1', '180.eb1', '180.ee1', '180.fa1', '270.bn1', '270.bw1', '270.by1', '360.cd1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [482808988, 87661065003, 224184, 462320323320, 143975, 80787, 355462956984, 375138230375], 'label': '77760.bo.90.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '90.bb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.bb1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246056361
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1440.j1', '1440.n1', '1440.p1', '2160.n1', '2160.br1', '2160.bt1', '2160.bw1', '2160.ca1'], 'contains': ['8640.m1', '12960.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [280259481600, 193999277493, 693], 'label': '77760.bo.4320.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '4320.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.k1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 246056362
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.c1', '1440.b1', '1440.k1', '2160.bn1', '2160.cb1', '2160.cj1', '2160.co1', '2160.cr1'], 'contains': ['8640.a1', '12960.f1', '12960.i1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [143975, 80787, 143304], 'label': '77760.bo.4320.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1440.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '4320.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.l1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056363
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.d1', '1440.b1', '1440.l1', '2160.cc1', '2160.ck1'], 'contains': ['8640.b1', '12960.f1', '12960.j1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [80787, 143304, 179159], 'label': '77760.bo.4320.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1440.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '4320.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.m1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056364
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.dd1', '1440.k1', '1440.m1', '1440.n1', '2160.bh1', '2160.cd1', '2160.ch1', '2160.cl1', '2160.cn1', '2160.cp1', '2160.cs1'], 'contains': ['8640.f1', '12960.g1', '12960.i1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [179012, 355419504452, 178680], 'label': '77760.bo.4320.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '4320.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.n1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056365
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.z1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.de1', '1440.k1', '1440.m1', '2160.ce1', '2160.cq1', '2160.ct1'], 'contains': ['8640.g1', '12960.h1', '12960.i1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [194518374212, 143975, 143304], 'label': '77760.bo.4320.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.v1', 'old_label': '4320.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.o1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056366
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.df1', '1440.l1', '1440.o1', '1440.p1', '2160.cf1', '2160.ci1', '2160.cm1'], 'contains': ['8640.h1', '12960.g1', '12960.j1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [355419504452, 224184, 224612], 'label': '77760.bo.4320.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.x1', 'old_label': '4320.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.p1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056367
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.dg1', '1440.l1', '1440.o1', '2160.cg1'], 'contains': ['8640.i1', '12960.h1', '12960.j1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [355419549955, 224184, 224612], 'label': '77760.bo.4320.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.u1', 'old_label': '4320.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.q1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056368
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.ee1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1440.q1', '1440.r1', '1440.s1', '1440.v1', '2160.o1', '2160.bj1', '2160.cb1', '2160.cu1', '2160.cu2', '2160.cx1', '2160.cx2', '2160.dc1', '2160.dc2', '2160.dj1', '2160.dj2'], 'contains': ['8640.a1', '12960.k1', '12960.l1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [442641386187, 143975, 80787], 'label': '77760.bo.4320.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '4320.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.r1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056369
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.ef1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1440.s1', '1440.t1', '1440.u1', '1440.w1', '2160.cc1', '2160.dd1', '2160.dd2', '2160.dk1', '2160.dk2'], 'contains': ['8640.b1', '12960.k1', '12960.m1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [442641386284, 80787, 179159], 'label': '77760.bo.4320.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.k1', 'old_label': '4320.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.s1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056370
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '240.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.eg1', '1440.q1', '1440.t1', '1440.z1', '2160.p1', '2160.bo1', '2160.cy1', '2160.de1', '2160.dx1'], 'contains': ['8640.c1', '12960.k1', '12960.n1', '12960.o1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [174436496787, 80787, 375138086400], 'label': '77760.bo.4320.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '4320.t1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.t1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056371
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.h1', '30.k1'], 'contains': ['180.cd1', '180.cf1', '180.co1', '180.dx1', '180.ec1', '180.ef1', '180.fb1', '270.bn1', '270.bx1', '270.bz1', '360.ce1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [448908278999, 262496506050, 462320323467, 19679028004, 461841050404, 80787, 143304, 179159], 'label': '77760.bo.90.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '90.bc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.bc1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246056372
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.q1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.eh1', '1440.q1', '1440.r1', '1440.u1', '1440.x1', '2160.q1', '2160.cz1', '2160.df1'], 'contains': ['8640.d1', '12960.k1', '12960.p1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [518963904, 442641024000, 80787], 'label': '77760.bo.4320.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.f1', 'old_label': '4320.u1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.u1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056373
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.ei1', '1440.r1', '1440.t1', '1440.u1', '1440.y1', '2160.dg1'], 'contains': ['8640.e1', '12960.k1', '12960.q1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [442641024000, 80787, 519235228], 'label': '77760.bo.4320.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.bg1', 'old_label': '4320.v1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.v1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056374
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.ej1', '1440.q1', '1440.bb1', '2160.a1', '2160.r1', '2160.cd1', '2160.cv1', '2160.da1', '2160.dh1', '2160.dy1'], 'contains': ['8640.f1', '12960.l1', '12960.n1', '12960.p1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [174436461504, 80880, 375138086400], 'label': '77760.bo.4320.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '4320.w1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.w1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056375
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.q1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.ek1', '1440.q1', '1440.ba1', '2160.ce1', '2160.cw1', '2160.db1'], 'contains': ['8640.g1', '12960.l1', '12960.o1', '12960.p1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [174436496787, 143975, 375138230375], 'label': '77760.bo.4320.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.bz1', 'old_label': '4320.x1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.x1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056376
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.el1', '1440.t1', '1440.bd1', '2160.cf1', '2160.di1', '2160.dz1'], 'contains': ['8640.h1', '12960.m1', '12960.n1', '12960.q1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [375138311012, 174436416000, 224612], 'label': '77760.bo.4320.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ce1', 'old_label': '4320.y1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.y1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056377
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.em1', '1440.t1', '1440.bc1', '2160.cg1'], 'contains': ['8640.i1', '12960.m1', '12960.o1', '12960.q1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [519235467, 442641386284, 179159], 'label': '77760.bo.4320.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '720.br1', 'old_label': '4320.z1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.z1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056378
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '240.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.en1', '1440.v1', '1440.w1', '1440.x1', '1440.y1', '1440.z1', '2160.s1', '2160.bp1', '2160.dm1', '2160.dr1', '2160.dx1'], 'contains': ['8640.c1', '12960.k1', '12960.r1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [188331171987, 80787, 375138086400], 'label': '77760.bo.4320.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '4320.ba1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.ba1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056379
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.eo1', '1440.v1', '1440.ba1', '1440.bb1', '2160.b1', '2160.t1', '2160.ch1', '2160.dl1', '2160.dn1', '2160.ds1', '2160.dy1'], 'contains': ['8640.f1', '12960.l1', '12960.r1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [143975, 188331091200, 375138230375], 'label': '77760.bo.4320.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '4320.bb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.bb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056380
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.ep1', '1440.w1', '1440.bc1', '1440.bd1', '2160.ci1', '2160.dt1', '2160.dz1'], 'contains': ['8640.h1', '12960.m1', '12960.r1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [375138265559, 188331091200, 179159], 'label': '77760.bo.4320.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.x1', 'old_label': '4320.bc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.bc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056381
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '480.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1440.z1', '1440.ba1', '1440.bc1', '2160.bq1', '2160.do1'], 'contains': ['8640.j1', '12960.o1', '12960.r1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 80, 'diagramx': None, 'generators': [93448938387, 174400173604, 83462400], 'label': '77760.bo.4320.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.h1', 'old_label': '4320.bd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.bd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056382
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.i1', '30.l1', '45.a1'], 'contains': ['180.cj1', '180.ck1', '180.cn1', '180.es1', '180.ev1', '180.ey1', '180.ez1', '270.bo1', '270.ca1', '270.cb1', '360.ch1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [80787, 143304, 375138172205, 87661140722, 80880, 355462911480, 462320046985, 482808988], 'label': '77760.bo.90.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '90.bd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.bd1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246056383
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1440.x1', '1440.ba1', '1440.bb1', '2160.c1', '2160.dp1', '2160.du1'], 'contains': ['8640.k1', '12960.p1', '12960.r1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [174400444920, 93449036612, 83462400], 'label': '77760.bo.4320.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1', 'old_label': '4320.be1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.be1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056384
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1440.y1', '1440.bc1', '1440.bd1', '2160.dv1'], 'contains': ['8640.l1', '12960.q1', '12960.r1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [93449001331, 83462400, 174400409544], 'label': '77760.bo.4320.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.bp1', 'old_label': '4320.bf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.bf1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056385
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '240.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1440.z1', '1440.bb1', '1440.bd1', '2160.d1', '2160.br1', '2160.dq1', '2160.dw1', '2160.ea1'], 'contains': ['8640.m1', '12960.n1', '12960.r1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [174400128000, 83462400, 93448857600], 'label': '77760.bo.4320.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '4320.bg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.bg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056386
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.fy1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.e1', '1440.be1', '1440.bf1', '2160.u1', '2160.bk1', '2160.cj1', '2160.dj1', '2160.dj2', '2160.eb1', '2160.eb2', '2160.ec1', '2160.ec2', '2160.ed1', '2160.ed2', '2160.ef1', '2160.eg1', '2160.eh1', '2160.ej1', '2160.ek1', '2160.el1', '2160.em1', '2160.en1', '2160.eo1', '2160.ep1', '2160.eq1', '2160.fb1'], 'contains': ['8640.a1', '12960.s1', '12960.t1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [80880, 80787, 274467916948], 'label': '77760.bo.4320.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '4320.bh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.bh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056387
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.fz1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.f1', '1440.be1', '1440.bg1', '2160.ck1', '2160.dk1', '2160.dk2', '2160.ee1', '2160.ee2', '2160.ei1', '2160.er1', '2160.es1', '2160.et1', '2160.eu1', '2160.fc1'], 'contains': ['8640.b1', '12960.s1', '12960.u1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [274467962404, 80787, 179159], 'label': '77760.bo.4320.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bi1', 'old_label': '4320.bi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.bi1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056388
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.cj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.o1', '1080.if1', '1440.bf1', '1440.bg1', '1440.bh1', '2160.v1', '2160.bs1', '2160.dx1', '2160.ew1', '2160.ey1'], 'contains': ['8640.c1', '12960.s1', '12960.v1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [113566924800, 88176256804, 80787], 'label': '77760.bo.4320.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '4320.bj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.bj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056389
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['432.p1', '1080.ig1', '1440.bf1', '1440.bi1', '2160.e1', '2160.w1', '2160.cl1', '2160.dy1', '2160.ev1', '2160.ex1', '2160.ez1'], 'contains': ['8640.f1', '12960.t1', '12960.v1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [368392291175, 442637757387, 143975], 'label': '77760.bo.4320.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '4320.bk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.bk1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056390
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.q1', '1080.ih1', '1440.bg1', '1440.bj1', '2160.cm1', '2160.dz1', '2160.fa1'], 'contains': ['8640.h1', '12960.u1', '12960.v1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [113566924800, 88176390359, 179159], 'label': '77760.bo.4320.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ce1', 'old_label': '4320.bl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.bl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056391
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1440.bh1', '1440.bi1', '1440.bj1', '2160.f1', '2160.bt1', '2160.ea1', '2160.fk1', '2160.fl1', '2160.fm1', '2160.fn1', '2160.fo1'], 'contains': ['8640.m1', '12960.v1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 10, 'diagramx': None, 'generators': [280259481600, 482630400, 193999276800], 'label': '77760.bo.4320.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '4320.bm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.bm1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246056392
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.gi1', '1440.bk1', '1440.bl1', '1440.bm1', '2160.a1', '2160.x1', '2160.cn1', '2160.dl1', '2160.ev1', '2160.fp1', '2160.gh1'], 'contains': ['8640.f1', '12960.w1', '12960.x1', '12960.y1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [143975, 375138270474, 174436416000], 'label': '77760.bo.4320.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '4320.bn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.bn1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056393
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['18.c1', '18.f1', '18.h1', '18.j1', '18.k1', '27.a1', '54.e1', '90.f1', '135.b1'], 'core': '36.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [85805, 93924236159, 80787, 462320046985, 693], 'label': '77760.bo.9.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '9.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
  • id: 246056452
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.hy1', '1440.da1', '1440.dh1', '2160.cm1', '2160.di1', '2160.dt1'], 'contains': ['8640.h1', '12960.bu1', '12960.bv1', '12960.bx1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [143731, 368392147650, 442637676744], 'label': '77760.bo.4320.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ce1', 'old_label': '4320.do1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.do1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056394
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['45.b1'], 'contains': ['180.cp1', '180.cs1', '180.cx1', '180.da1', '180.db1', '180.dj1', '180.dk1', '180.ei1', '180.ej1', '270.bp1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [461841090505, 462320323320, 143975, 19678982548, 80880, 80787, 448908283914, 143304], 'label': '77760.bo.90.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '90.be1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.be1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246056395
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.gb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1440.bk1', '1440.bn1', '1440.bp1', '1440.br1', '2160.o1', '2160.bl1', '2160.co1', '2160.cu1', '2160.cu2', '2160.eb1', '2160.eb2', '2160.fq1', '2160.fq2', '2160.gi1', '2160.gi2'], 'contains': ['8640.a1', '12960.w1', '12960.z1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 375138270474, 80787], 'label': '77760.bo.4320.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '4320.bo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.bo1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056396
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.cd1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.gn1', '1440.bk1', '1440.bo1', '1440.bs1', '1440.bu1', '2160.p1', '2160.y1', '2160.bu1', '2160.dm1', '2160.ew1', '2160.fr1', '2160.gj1'], 'contains': ['8640.c1', '12960.x1', '12960.z1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [518964004, 442641109705, 80787], 'label': '77760.bo.4320.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '4320.bp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.bp1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056397
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.w1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.go1', '1440.bk1', '1440.bq1', '1440.bt1', '1440.bv1', '2160.q1', '2160.fs1', '2160.gk1'], 'contains': ['8640.d1', '12960.y1', '12960.z1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [174436416243, 375138172555, 80787], 'label': '77760.bo.4320.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.f1', 'old_label': '4320.bq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.bq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056398
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.gk1', '1440.bm1', '1440.bn1', '2160.b1', '2160.z1', '2160.cp1', '2160.cv1', '2160.ev1', '2160.ft1', '2160.ga1'], 'contains': ['8640.f1', '12960.w1', '12960.bb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [179012, 442641300482, 442162022400], 'label': '77760.bo.4320.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '4320.br1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.br1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056399
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.gp1', '1440.bo1', '1440.bw1', '1440.bx1', '2160.g1', '2160.r1', '2160.cn1', '2160.dn1', '2160.ex1', '2160.fz1', '2160.ga1'], 'contains': ['8640.f1', '12960.x1', '12960.ba1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [174436461504, 375138172205, 80880], 'label': '77760.bo.4320.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '4320.bs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.bs1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056400
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.bb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.gl1', '1440.bl1', '1440.bn1', '2160.cq1', '2160.cw1', '2160.fu1'], 'contains': ['8640.g1', '12960.w1', '12960.bc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [188331136563, 148, 375138172555], 'label': '77760.bo.4320.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.cb1', 'old_label': '4320.bt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.bt1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056401
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.n1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1440.bl1', '1440.bu1', '1440.bw1', '2160.bv1', '2160.do1', '2160.fv1'], 'contains': ['8640.j1', '12960.x1', '12960.bc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [174400208787, 456053073961, 93448857600], 'label': '77760.bo.4320.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.cb1', 'old_label': '4320.bu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.bu1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056402
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1440.bs1', '1440.bw1', '1440.bx1', '2160.h1', '2160.dp1', '2160.gb1'], 'contains': ['8640.k1', '12960.x1', '12960.bd1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [83548555, 93449036612, 174400307012], 'label': '77760.bo.4320.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.c1', 'old_label': '4320.bv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.bv1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056403
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1440.bm1', '1440.bt1', '2160.c1', '2160.fw1', '2160.gb1'], 'contains': ['8640.k1', '12960.y1', '12960.bb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [93449139388, 83467561, 174400352515], 'label': '77760.bo.4320.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.a1', 'old_label': '4320.bw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.bw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056404
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.bh1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1440.bm1', '1440.bu1', '1440.bx1', '2160.d1', '2160.i1', '2160.bw1', '2160.dq1', '2160.fk1', '2160.fx1', '2160.gc1'], 'contains': ['8640.m1', '12960.x1', '12960.bb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [83548555, 174400128000, 93448857600], 'label': '77760.bo.4320.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '4320.bx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.bx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056405
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['30.j1', '45.b1'], 'contains': ['180.cp2', '180.cq1', '180.cu1', '180.cx1', '180.cy1', '180.dd1', '180.de1', '180.di1', '180.dm1', '180.eh1', '180.eq1', '270.bq1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [461841090505, 143975, 80787, 143304, 19678982548, 448908283914, 80880, 462320328386], 'label': '77760.bo.90.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '90.bf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.bf1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246056406
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1440.bl1', '1440.bt1', '2160.fy1'], 'contains': ['8640.n1', '12960.y1', '12960.bc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2880, 'diagramx': None, 'generators': [93449219787, 174400307012, 83467561], 'label': '77760.bo.4320.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '720.fa1', 'old_label': '4320.by1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.by1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056407
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gk1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1440.bo1', '1440.bq1', '1440.br1', '1440.by1', '2160.ba1', '2160.bj1', '2160.co1', '2160.cx1', '2160.cx2', '2160.ec1', '2160.ec2', '2160.ge1', '2160.ge2', '2160.gi1', '2160.gi2'], 'contains': ['8640.a1', '12960.z1', '12960.ba1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [442641109705, 80880, 80787], 'label': '77760.bo.4320.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '4320.bz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.bz1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246056408
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.ch1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.gr1', '1440.bn1', '1440.bt1', '1440.bu1', '1440.by1', '2160.s1', '2160.bb1', '2160.bx1', '2160.cy1', '2160.ew1', '2160.gd1', '2160.gj1'], 'contains': ['8640.c1', '12960.z1', '12960.bb1', '12960.bc1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [442162022400, 442641301050, 80787], 'label': '77760.bo.4320.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '4320.ca1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.ca1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056409
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.gs1', '1440.bp1', '1440.bs1', '1440.bv1', '1440.by1', '2160.bc1', '2160.cz1', '2160.gk1'], 'contains': ['8640.d1', '12960.z1', '12960.bd1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [188331136563, 375138172205, 80787], 'label': '77760.bo.4320.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.g1', 'old_label': '4320.cb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.cb1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246056410
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.gt1', '1440.bx1', '1440.by1', '2160.j1', '2160.t1', '2160.cp1', '2160.da1', '2160.ex1', '2160.gf1', '2160.gh1'], 'contains': ['8640.f1', '12960.ba1', '12960.bb1', '12960.bd1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [143975, 188331091200, 375138172555], 'label': '77760.bo.4320.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '4320.cc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.cc1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056411
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.gu1', '1440.bw1', '1440.by1', '2160.cq1', '2160.db1', '2160.gg1'], 'contains': ['8640.g1', '12960.ba1', '12960.bc1', '12960.bd1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [188331171987, 143975, 375138172555], 'label': '77760.bo.4320.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.cb1', 'old_label': '4320.cd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.cd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056412
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.bo1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.gw1', '1440.bz1', '1440.ca1', '1440.cb1', '1440.cc1', '1440.cd1', '2160.y1', '2160.bo1', '2160.dr1', '2160.ey1', '2160.gd1'], 'contains': ['8640.c1', '12960.be1', '12960.bf1', '12960.bg1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [518964004, 442641386755, 80787], 'label': '77760.bo.4320.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '4320.ce1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.ce1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056413
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.ga1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1440.bz1', '1440.ce1', '1440.cf1', '1440.cg1', '2160.ba1', '2160.bl1', '2160.cb1', '2160.dc1', '2160.dc2', '2160.ed1', '2160.ed2', '2160.fq1', '2160.fq2', '2160.ge1', '2160.ge2'], 'contains': ['8640.a1', '12960.be1', '12960.bh1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [375138087093, 143975, 80787], 'label': '77760.bo.4320.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '4320.cf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.cf1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056414
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.ga1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1440.ca1', '1440.cg1', '1440.ch1', '1440.ci1', '2160.cc1', '2160.dd1', '2160.dd2', '2160.ee1', '2160.ee2'], 'contains': ['8640.b1', '12960.be1', '12960.bi1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [442641386755, 80787, 179159], 'label': '77760.bo.4320.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '4320.cg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.cg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056415
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.bp1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.gz1', '1440.cd1', '1440.ce1', '1440.ch1', '2160.bb1', '2160.bp1', '2160.de1', '2160.ey1', '2160.fr1'], 'contains': ['8640.c1', '12960.be1', '12960.bj1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [442641386755, 442162022400, 80787], 'label': '77760.bo.4320.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.r1', 'old_label': '4320.ch1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.ch1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056416
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['45.b1'], 'contains': ['180.cp2', '180.cr1', '180.cv1', '180.cz1', '180.db1', '180.dh1', '180.do1', '180.eg1', '270.br1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [448908278999, 461841090505, 143975, 19678982548, 80880, 80787, 462320328386, 143304], 'label': '77760.bo.90.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '90.bg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.bg1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246056417
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.ba1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.ha1', '1440.cb1', '1440.ce1', '1440.cf1', '1440.ci1', '2160.bc1', '2160.df1', '2160.fs1'], 'contains': ['8640.d1', '12960.be1', '12960.bk1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [188331270212, 375138087093, 80787], 'label': '77760.bo.4320.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.i1', 'old_label': '4320.ci1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.ci1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056418
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.hb1', '1440.cc1', '1440.cf1', '1440.ch1', '1440.ci1', '2160.dg1'], 'contains': ['8640.e1', '12960.be1', '12960.bl1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [442641386755, 80787, 442162201559], 'label': '77760.bo.4320.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '720.di1', 'old_label': '4320.cj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.cj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056419
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.p1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.he1', '1440.bz1', '1440.ck1', '2160.g1', '2160.x1', '2160.cd1', '2160.ds1', '2160.ez1', '2160.ft1', '2160.gf1'], 'contains': ['8640.f1', '12960.bf1', '12960.bh1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [375138087093, 174436416243, 148], 'label': '77760.bo.4320.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '4320.ck1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.ck1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056420
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.t1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.hf1', '1440.bz1', '1440.cj1', '2160.ce1', '2160.fu1', '2160.gg1'], 'contains': ['8640.g1', '12960.bg1', '12960.bh1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [174436496787, 375138087093, 143975], 'label': '77760.bo.4320.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.bz1', 'old_label': '4320.cl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.cl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056421
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.hg1', '1440.ca1', '1440.cm1', '2160.cf1', '2160.dt1', '2160.fa1'], 'contains': ['8640.h1', '12960.bf1', '12960.bi1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [375138087093, 174436416000, 224612], 'label': '77760.bo.4320.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ce1', 'old_label': '4320.cm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.cm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056422
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.hh1', '1440.ca1', '1440.cl1', '2160.cg1'], 'contains': ['8640.i1', '12960.bg1', '12960.bi1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [442641341252, 519280684, 224612], 'label': '77760.bo.4320.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '720.br1', 'old_label': '4320.cn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.cn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056423
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1440.cd1', '1440.cj1', '1440.cl1', '2160.bq1', '2160.fv1'], 'contains': ['8640.j1', '12960.bg1', '12960.bj1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [456053069398, 93448938387, 174400128000], 'label': '77760.bo.4320.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.bu1', 'old_label': '4320.co1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.co1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056424
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1440.cb1', '1440.ck1', '2160.h1', '2160.du1', '2160.fw1'], 'contains': ['8640.k1', '12960.bf1', '12960.bk1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [93448857748, 83462998, 174400128148], 'label': '77760.bo.4320.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.i1', 'old_label': '4320.cp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.cp1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056425
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1440.cc1', '1440.cm1', '2160.dv1'], 'contains': ['8640.l1', '12960.bf1', '12960.bl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [456053069398, 174400307159, 93448857600], 'label': '77760.bo.4320.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '720.di1', 'old_label': '4320.cq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.cq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056426
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.bi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1440.cd1', '1440.ck1', '1440.cm1', '2160.i1', '2160.br1', '2160.dw1', '2160.fl1', '2160.fx1'], 'contains': ['8640.m1', '12960.bf1', '12960.bj1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [83462998, 174400128000, 93448857600], 'label': '77760.bo.4320.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.r1', 'old_label': '4320.cr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.cr1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056427
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['30.i1', '45.b1'], 'contains': ['180.cp1', '180.cq1', '180.cr1', '180.ct1', '180.cw1', '180.dc1', '180.de1', '180.dg1', '180.dg2', '180.ds1', '180.en1', '270.bs1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [448908278999, 461841090505, 462320323320, 143975, 19678982548, 80880, 80787, 143304], 'label': '77760.bo.90.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '90.bh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.bh1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246056428
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1440.cb1', '1440.cj1', '2160.fy1'], 'contains': ['8640.n1', '12960.bg1', '12960.bk1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2880, 'diagramx': None, 'generators': [456053069398, 93448938387, 174400128148], 'label': '77760.bo.4320.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '720.fd1', 'old_label': '4320.cs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.cs1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056429
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1440.cc1', '1440.cl1'], 'contains': ['8640.o1', '12960.bg1', '12960.bl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2880, 'diagramx': None, 'generators': [456053069398, 93448938387, 174400307159], 'label': '77760.bo.4320.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1440.cc1', 'old_label': '4320.ct1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.ct1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056430
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.s1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.hi1', '1440.ce1', '1440.cj1', '1440.ck1', '2160.j1', '2160.z1', '2160.ch1', '2160.dh1', '2160.ez1', '2160.fp1', '2160.fz1'], 'contains': ['8640.f1', '12960.bh1', '12960.bj1', '12960.bk1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [375138087093, 143975, 188331091200], 'label': '77760.bo.4320.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '4320.cu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.cu1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056431
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.hj1', '1440.ch1', '1440.cl1', '1440.cm1', '2160.ci1', '2160.di1', '2160.fa1'], 'contains': ['8640.h1', '12960.bi1', '12960.bj1', '12960.bl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [442162022400, 442641341252, 224612], 'label': '77760.bo.4320.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.x1', 'old_label': '4320.cv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.cv1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056432
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.g1', '1440.cn1', '1440.co1', '1440.cp1', '2160.u1', '2160.bm1', '2160.cr1', '2160.cu1', '2160.cu2', '2160.ef1', '2160.ge1', '2160.ge2', '2160.gl1'], 'contains': ['8640.a1', '12960.bm1', '12960.bn1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [143975, 274468002505, 80787], 'label': '77760.bo.4320.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '4320.cw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.cw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056433
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.hl1', '1440.cn1', '1440.cq1', '1440.cr1', '2160.e1', '2160.bd1', '2160.cs1', '2160.cv1', '2160.dl1', '2160.fz1', '2160.gf1'], 'contains': ['8640.f1', '12960.bm1', '12960.bp1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [113566924948, 88176216811, 148], 'label': '77760.bo.4320.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '4320.cx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.cx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056434
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.hm1', '1440.cn1', '1440.cq1', '2160.ct1', '2160.cw1', '2160.gg1'], 'contains': ['8640.g1', '12960.bm1', '12960.bq1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [113567005587, 179012, 88176350010], 'label': '77760.bo.4320.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.cm1', 'old_label': '4320.cy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.cy1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056435
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.h1', '1440.cp1', '1440.cs1', '2160.be1', '2160.bk1', '2160.cr1', '2160.cx1', '2160.cx2', '2160.eg1', '2160.fq1', '2160.fq2', '2160.gl1'], 'contains': ['8640.a1', '12960.bn1', '12960.bo1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [143975, 274468135825, 80787], 'label': '77760.bo.4320.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '4320.cz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.cz1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246056436
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.ho1', '1440.cn1', '1440.cs1', '1440.ct1', '1440.cu1', '2160.v1', '2160.bf1', '2160.by1', '2160.cy1', '2160.dm1', '2160.fr1', '2160.gd1'], 'contains': ['8640.c1', '12960.bn1', '12960.bp1', '12960.bq1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [113566924800, 88176252092, 80787], 'label': '77760.bo.4320.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '4320.da1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.da1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056437
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.hp1', '1440.co1', '1440.cs1', '1440.ct1', '2160.bg1', '2160.cz1', '2160.fs1'], 'contains': ['8640.d1', '12960.bn1', '12960.br1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [368392152509, 442637476080, 80787], 'label': '77760.bo.4320.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ba1', 'old_label': '4320.db1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.db1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246056438
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.k1', '45.b1'], 'contains': ['180.cs1', '180.cu1', '180.cv1', '180.cw1', '180.df1', '180.dl1', '180.dn1', '180.dp1', '180.dw1', '180.ed1', '180.ex1', '270.bw1', '270.bx1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [448908278999, 461841004948, 462320323320, 143975, 19678982548, 80880, 80787, 143304], 'label': '77760.bo.90.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '90.bi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.bi1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246056439
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.hq1', '1440.cs1', '1440.cv1', '1440.cw1', '2160.k1', '2160.w1', '2160.cs1', '2160.da1', '2160.dn1', '2160.fp1', '2160.ft1'], 'contains': ['8640.f1', '12960.bo1', '12960.bp1', '12960.br1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [368392152509, 442637395200, 80880], 'label': '77760.bo.4320.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '4320.dc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.dc1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056440
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.hr1', '1440.cs1', '1440.cv1', '2160.ct1', '2160.db1', '2160.fu1'], 'contains': ['8640.g1', '12960.bo1', '12960.bq1', '12960.br1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [88176216509, 80880, 113566970163], 'label': '77760.bo.4320.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.cm1', 'old_label': '4320.dd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.dd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056441
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1440.cq1', '1440.cu1', '1440.cv1', '2160.bz1', '2160.do1', '2160.fv1'], 'contains': ['8640.j1', '12960.bp1', '12960.bq1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [280259562387, 482635561, 193999357587], 'label': '77760.bo.4320.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.cb1', 'old_label': '4320.de1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.de1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056442
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1440.ct1', '1440.cv1', '1440.cw1', '2160.l1', '2160.dp1', '2160.fw1'], 'contains': ['8640.k1', '12960.bp1', '12960.br1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [482849425, 280259625575, 193999420775], 'label': '77760.bo.4320.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.c1', 'old_label': '4320.df1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.df1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056443
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1440.cr1', '1440.cu1', '1440.cw1', '2160.f1', '2160.m1', '2160.ca1', '2160.dq1', '2160.fx1'], 'contains': ['8640.m1', '12960.bp1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [280259481600, 482849425, 193999276800], 'label': '77760.bo.4320.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '4320.dg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.dg1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246056444
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1440.ct1', '1440.cv1', '2160.fy1'], 'contains': ['8640.n1', '12960.bq1', '12960.br1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 8640, 'diagramx': None, 'generators': [482635561, 280259527104, 193999357587], 'label': '77760.bo.4320.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2160.fy1', 'old_label': '4320.dh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.dh1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056445
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.i1', '1440.cx1', '1440.cy1', '1440.cz1', '2160.be1', '2160.bm1', '2160.cj1', '2160.dc1', '2160.dc2', '2160.eh1', '2160.gi1', '2160.gi2', '2160.gl1'], 'contains': ['8640.a1', '12960.bs1', '12960.bt1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [274468060348, 143975, 80787], 'label': '77760.bo.4320.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '4320.di1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.di1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056446
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.j1', '1440.cz1', '1440.da1', '1440.db1', '2160.ck1', '2160.dd1', '2160.dd2', '2160.ei1'], 'contains': ['8640.b1', '12960.bs1', '12960.bu1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [274468060348, 80787, 179159], 'label': '77760.bo.4320.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '4320.dj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.dj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056447
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.hu1', '1440.cx1', '1440.da1', '1440.dc1', '1440.dd1', '1440.de1', '2160.bf1', '2160.bs1', '2160.de1', '2160.dr1', '2160.gj1'], 'contains': ['8640.c1', '12960.bs1', '12960.bv1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [88176292437, 113566924800, 80787], 'label': '77760.bo.4320.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '4320.dk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.dk1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056448
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.hv1', '1440.cx1', '1440.cy1', '1440.db1', '1440.dc1', '1440.df1', '1440.df2', '2160.bg1', '2160.df1', '2160.gk1'], 'contains': ['8640.d1', '12960.bs1', '12960.bw1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [88176292437, 80787, 113567068775], 'label': '77760.bo.4320.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.q1', 'old_label': '4320.dl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.dl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056449
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '90.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.l1', '45.b1'], 'contains': ['180.cz1', '180.da1', '180.dc1', '180.dd1', '180.df1', '180.ek1', '180.eu1', '180.ew1', '270.ca1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [143975, 80787, 143304, 19678982548, 448908283914, 80880, 461841004948, 462320328386], 'label': '77760.bo.90.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '90.bj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.bj1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246056450
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.hw1', '1440.cy1', '1440.da1', '1440.db1', '1440.dd1', '1440.df1', '1440.df2', '2160.dg1'], 'contains': ['8640.e1', '12960.bs1', '12960.bx1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [88176292437, 113567103959, 80787], 'label': '77760.bo.4320.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2160.dg1', 'old_label': '4320.dm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.dm1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056451
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.hx1', '1440.cx1', '1440.dg1', '2160.k1', '2160.bd1', '2160.cl1', '2160.dh1', '2160.ds1', '2160.ga1', '2160.gh1'], 'contains': ['8640.f1', '12960.bt1', '12960.bv1', '12960.bw1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [113566924800, 179012, 88176211650], 'label': '77760.bo.4320.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '4320.dn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.dn1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056453
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1440.dc1', '1440.dg1', '2160.l1', '2160.du1', '2160.gb1'], 'contains': ['8640.k1', '12960.bv1', '12960.bw1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [482854584, 280259706115, 193999558588], 'label': '77760.bo.4320.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.i1', 'old_label': '4320.dp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.dp1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056454
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1440.dd1', '1440.dh1', '2160.dv1'], 'contains': ['8640.l1', '12960.bv1', '12960.bx1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [482854584, 193999501412, 280259706212], 'label': '77760.bo.4320.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '720.di1', 'old_label': '4320.dq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.dq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246056455
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4320.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1440.de1', '1440.dg1', '1440.dh1', '2160.m1', '2160.bt1', '2160.dw1', '2160.gc1'], 'contains': ['8640.m1', '12960.bv1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [280259481600, 482854584, 193999276800], 'label': '77760.bo.4320.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '4320.dr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.dr1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246056456
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.a1', '1620.bc1', '1620.be1', '2430.a1', '2430.e1', '2430.g1'], 'contains': ['9720.b2', '9720.d1', '9720.e1', '9720.bb1', '9720.bd1', '9720.bm1', '9720.bn1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [183845, 7185207845, 462320190245, 19678982400], 'label': '77760.bo.4860.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '4860.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056457
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.b1', '1620.bd1', '1620.bf1', '2430.d1', '2430.g1'], 'contains': ['9720.b2', '9720.f1', '9720.g1', '9720.bc1', '9720.bd1', '9720.bo1', '9720.bp1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [7185029309, 19678982400, 462320328958, 322558], 'label': '77760.bo.4860.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056458
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.c1', '1620.bg1', '1620.bh1', '2430.c1', '2430.d1', '2430.h1'], 'contains': ['9720.b1', '9720.g1', '9720.h1', '9720.z1', '9720.ba1', '9720.bk1', '9720.bl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [86155, 87182006155, 375138172555, 482716346], 'label': '77760.bo.4860.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056459
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['540.c1', '1620.d1', '1620.bi1', '1620.bk1', '2430.b1', '2430.d1', '2430.i1'], 'contains': ['9720.b1', '9720.c1', '9720.f1', '9720.w1', '9720.y1', '9720.bi1', '9720.bs1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [87261753600, 456053154955, 85805, 83462400], 'label': '77760.bo.4860.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056460
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.a1', 'complements': ['720.a1', '720.bk1', '720.cm1', '720.ft1', '720.bj1', '720.bh1', '720.fh1', '720.bg1', '720.fh2', '720.fg1', '720.cl1', '720.fn2', '720.fn1', '720.fm1', '720.fq1'], 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '36.q1', '36.r1', '54.a1', '54.f1'], 'contains': ['216.a1', '648.p1', '1080.es1', '1620.gk1'], 'core': '108.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [93924230400, 462320006400], 'label': '77760.bo.108.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': ['36.a1'], 'normal_contains': ['216.a1'], 'normalizer': '1.a1', 'old_label': '108.a1', 'projective_image': '77760.bo', 'quotient_action_image': '1.1', 'quotient_action_kernel': '108.17', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '108.a1', 'subgroup_fusion': None, 'weyl_group': '720.763'}
  • id: 246056461
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.e1', '1620.bj1', '1620.bl1', '2430.a1', '2430.d1', '2430.j1'], 'contains': ['9720.a1', '9720.a2', '9720.b2', '9720.c1', '9720.h1', '9720.u1', '9720.u2', '9720.v1', '9720.x1', '9720.bh1', '9720.bq1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [461841090505, 357597, 19678982400, 462320363997], 'label': '77760.bo.4860.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056462
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.e2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.e2', '1620.bj2', '1620.bl2', '2430.b1', '2430.c1', '2430.j1'], 'contains': ['9720.a1', '9720.a2', '9720.b1', '9720.c2', '9720.h1', '9720.u1', '9720.u3', '9720.v2', '9720.x2', '9720.bh2', '9720.bq1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [461841223825, 462320225425, 19678982400, 40585], 'label': '77760.bo.4860.e2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.e2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.e2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056463
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.ck2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.f1', '1620.k1', '1620.bm1', '1620.bn1', '2430.b1', '2430.e1', '2430.h1'], 'contains': ['9720.b1', '9720.d1', '9720.i1', '9720.z1', '9720.be1', '9720.bj1', '9720.cd1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [86155, 482716555, 87182006155, 375138172555], 'label': '77760.bo.4860.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '4860.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056464
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.ck2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.d1', '1620.g1', '1620.bo1', '1620.bp1', '2430.c1', '2430.e1', '2430.i1'], 'contains': ['9720.b1', '9720.e1', '9720.w1', '9720.bf1', '9720.br1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [87261753600, 5161, 456053073961, 83462400], 'label': '77760.bo.4860.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '4860.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056465
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bd1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.h1', '1620.i1', '1620.j1', '1620.bq1', '1620.br1', '2430.d1', '2430.e1', '2430.j1'], 'contains': ['9720.b1', '9720.b2', '9720.i1', '9720.v1', '9720.v2', '9720.bg1', '9720.ce1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841223825, 462320225425, 219025, 19678982400], 'label': '77760.bo.4860.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '4860.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056466
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.l1', '1620.bs1', '1620.bw1', '2430.b1', '2430.g1'], 'contains': ['9720.c2', '9720.d1', '9720.f1', '9720.bm1', '9720.bo1', '9720.bv1', '9720.bx1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [462320092205, 183845, 7185207845, 19678982400], 'label': '77760.bo.4860.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056467
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.m1', '1620.bt1', '1620.bx1', '2430.c1', '2430.f1', '2430.g1'], 'contains': ['9720.c2', '9720.e1', '9720.g1', '9720.bn1', '9720.bp1', '9720.bw1', '9720.bx1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [183845, 7185029309, 19678982400, 462320011709], 'label': '77760.bo.4860.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056468
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.n1', '1620.bu1', '1620.by1', '2430.a1', '2430.b1', '2430.h1'], 'contains': ['9720.c1', '9720.d1', '9720.h1', '9720.bj1', '9720.bl1', '9720.bt1', '9720.bu1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [482716205, 277050, 375138172205, 87182197050], 'label': '77760.bo.4860.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.k1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056469
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.h1', '1620.o1', '1620.bv1', '1620.bz1', '2430.a1', '2430.f1', '2430.i1'], 'contains': ['9720.c1', '9720.e1', '9720.bi1', '9720.br1', '9720.by1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [87261753600, 83462998, 456053073961, 5759], 'label': '77760.bo.4860.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.l1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056470
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.p1', '1620.ca1', '1620.cb1', '2430.a1', '2430.c1', '2430.k1'], 'contains': ['9720.e1', '9720.h1', '9720.bz1', '9720.ca1', '9720.cc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [87181925066, 357597, 355938110666, 374659442397], 'label': '77760.bo.4860.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.m1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056471
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.a1', '36.c1', '54.d1'], 'contains': ['216.b1', '216.q1', '216.s1', '324.a1', '540.b1', '648.a1', '1080.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [45363, 462320328958, 322558, 174879210244], 'label': '77760.bo.108.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '108.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1', 'subgroup_fusion': None, 'weyl_group': '240.189'}
  • id: 246056472
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.r1', '1620.s1', '1620.t1', '1620.cc1', '1620.ce1', '2430.d1', '2430.f1', '2430.h1'], 'contains': ['9720.c1', '9720.g1', '9720.i1', '9720.bk1', '9720.bt1', '9720.cd1', '9720.cf1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [277050, 375138172205, 87182197050, 482907450], 'label': '77760.bo.4860.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.n1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056473
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.q1', '1620.u1', '1620.cd1', '1620.cf1', '2430.b1', '2430.f1', '2430.j1'], 'contains': ['9720.c1', '9720.c2', '9720.i1', '9720.bh1', '9720.bh2', '9720.ce1', '9720.cg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [183845, 19678982400, 448908001949, 462320046749], 'label': '77760.bo.4860.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '4860.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.o1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056474
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.v1', '1620.w1', '1620.x1', '1620.cg1', '1620.ch1', '2430.b1', '2430.d1', '2430.k1'], 'contains': ['9720.f1', '9720.h1', '9720.i1', '9720.bz1', '9720.cb1', '9720.ch1', '9720.ci1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [355938243842, 87181925066, 374659089866, 5066], 'label': '77760.bo.4860.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.p1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056475
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.ck2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.y1', '1620.z1', '1620.ci1', '1620.cj1', '2430.e1', '2430.f1', '2430.k1'], 'contains': ['9720.e1', '9720.i1', '9720.ca1', '9720.ch1', '9720.cj1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [87182277597, 355938463197, 357597, 374659442397], 'label': '77760.bo.4860.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '4860.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.q1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056476
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.ba1', '1620.ck1', '1620.co1', '2430.h1', '2430.i1', '2430.j1'], 'contains': ['9720.a1', '9720.b1', '9720.c1', '9720.j1', '9720.k1', '9720.l1', '9720.m1', '9720.n1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [362615, 85805, 375138172205, 87182197050], 'label': '77760.bo.4860.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.r1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056477
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.r2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1215.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1620.ck2', '1620.co2', '2430.g1', '2430.j1'], 'contains': ['9720.a2', '9720.b2', '9720.c2', '9720.j1', '9720.k1', '9720.l2', '9720.m2', '9720.n2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1215, 'diagramx': None, 'generators': [362615, 442641024000, 40585, 448908284158], 'label': '77760.bo.4860.r2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.r2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.r2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056478
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['972.a1', '1620.cl1', '1620.cp1', '2430.g1', '2430.h1'], 'contains': ['9720.d1', '9720.g1', '9720.k1', '9720.p1', '9720.s1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1215, 'diagramx': None, 'generators': [362615, 443120025600, 267845679358, 40585], 'label': '77760.bo.4860.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.s1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056479
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.k1', '1620.cm1', '1620.cq1', '2430.g1', '2430.i1', '2430.k1'], 'contains': ['9720.e1', '9720.f1', '9720.k1', '9720.q1', '9720.r1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1215, 'diagramx': None, 'generators': [482849425, 40585, 88695348625, 143304], 'label': '77760.bo.4860.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.t1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.t1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056480
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.bb1', '1620.cn1', '1620.cr1', '2430.h1', '2430.j1', '2430.k1'], 'contains': ['9720.h1', '9720.i1', '9720.k1', '9720.o1', '9720.t1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [274467916800, 268244524800, 85805, 143304], 'label': '77760.bo.4860.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '4860.u1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.u1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056481
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.cs1', '1620.ds1', '2430.j1', '2430.l1', '2430.o1'], 'contains': ['9720.l1', '9720.l2', '9720.m2', '9720.n1', '9720.o1', '9720.u2', '9720.u3', '9720.v1', '9720.bh2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [461841090505, 178680, 19678982400, 462320006400], 'label': '77760.bo.4860.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.v1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.v1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056482
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.b1', '36.d1', '54.d1'], 'contains': ['216.b1', '216.u1', '216.w1', '324.b1', '540.f1', '648.b1', '1080.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [174879411571, 224515, 85946, 462320328958], 'label': '77760.bo.108.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '108.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 246056483
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.v2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.cs2', '1620.ds2', '2430.j1', '2430.m1', '2430.n1'], 'contains': ['9720.l1', '9720.l2', '9720.m1', '9720.n2', '9720.o1', '9720.u1', '9720.v2', '9720.bh1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [462320092105, 461841090505, 178680, 19678982400], 'label': '77760.bo.4860.v2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.v2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.v2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056484
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['540.cs1', '1620.ct1', '1620.dt1', '2430.i1', '2430.m1', '2430.o1'], 'contains': ['9720.m1', '9720.n1', '9720.r1', '9720.w1', '9720.bi1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [87261753600, 83548555, 456053069398, 598], 'label': '77760.bo.4860.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.w1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.w1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056485
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.cu1', '1620.du1', '2430.h1', '2430.n1', '2430.o1'], 'contains': ['9720.m1', '9720.o1', '9720.s1', '9720.z1', '9720.bt1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [362615, 482952958, 87182282615, 375138086400], 'label': '77760.bo.4860.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.x1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.x1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056486
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1620.cv1', '1620.dv1', '1620.dx1', '2430.g1', '2430.l1', '2430.p1'], 'contains': ['9720.m2', '9720.p1', '9720.q1', '9720.bb1', '9720.bc1', '9720.bv1', '9720.bw1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [178680, 19678982400, 462320006400, 7185202680], 'label': '77760.bo.4860.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '4860.y1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.y1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056487
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1620.cw1', '1620.dw1', '2430.g1', '2430.o1'], 'contains': ['9720.m2', '9720.r1', '9720.s1', '9720.bd1', '9720.bx1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1215, 'diagramx': None, 'generators': [7185207845, 19678982400, 462320006400, 143304], 'label': '77760.bo.4860.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.z1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.z1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056488
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.co2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.cx1', '1620.dc1', '1620.dy1', '1620.dz1', '2430.h1', '2430.m1', '2430.p1'], 'contains': ['9720.m1', '9720.p1', '9720.t1', '9720.ba1', '9720.be1', '9720.bu1', '9720.cf1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [443120025600, 224184, 442641024000, 180667289784], 'label': '77760.bo.4860.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '4860.ba1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.ba1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056489
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.co2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.ct1', '1620.cy1', '1620.ea1', '1620.eb1', '2430.i1', '2430.n1', '2430.p1'], 'contains': ['9720.m1', '9720.q1', '9720.y1', '9720.bf1', '9720.by1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [87261753600, 456053069398, 83462998, 598], 'label': '77760.bo.4860.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '4860.bb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.bb1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056490
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.cz1', '1620.da1', '1620.db1', '1620.ec1', '1620.ed1', '2430.j1', '2430.o1', '2430.p1'], 'contains': ['9720.m1', '9720.m2', '9720.t1', '9720.x1', '9720.x2', '9720.bg1', '9720.cg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [461841004800, 19678982400, 462320006400, 143304], 'label': '77760.bo.4860.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '4860.bc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.bc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056531
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '5184.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.b1', '2592.f1', '2592.i1', '2592.o1'], 'contains': ['15552.a1', '25920.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [18764524800, 179159], 'label': '77760.bo.5184.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.m1', 'old_label': '5184.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.c1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 246056491
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.dd1', '1620.ee1', '2430.h1', '2430.l1', '2430.m1'], 'contains': ['9720.n1', '9720.o1', '9720.p1', '9720.bj1', '9720.bk1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [362615, 375138172205, 87182282615, 482907450], 'label': '77760.bo.4860.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.bd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.bd1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056492
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1620.de1', '1620.ef1', '2430.g1', '2430.m1'], 'contains': ['9720.n2', '9720.p1', '9720.r1', '9720.bm1', '9720.bp1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1215, 'diagramx': None, 'generators': [178680, 19678982400, 462320046842, 7185202680], 'label': '77760.bo.4860.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.be1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.be1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056493
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.b1', '36.e1', '36.f1', '54.a1', '54.b1', '54.c1'], 'contains': ['216.a1', '648.c1', '1080.j1', '1620.z1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87182277597, 274511462400, 357597], 'label': '77760.bo.108.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1', 'subgroup_fusion': None, 'weyl_group': '720.763'}
  • id: 246056494
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1620.df1', '1620.eg1', '2430.g1', '2430.n1', '2430.q1'], 'contains': ['9720.n2', '9720.q1', '9720.s1', '9720.bn1', '9720.bo1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1215, 'diagramx': None, 'generators': [462320092205, 7185207845, 19678982400, 143304], 'label': '77760.bo.4860.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.bf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.bf1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056495
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.cx1', '1620.dg1', '1620.eh1', '2430.i1', '2430.l1', '2430.q1'], 'contains': ['9720.n1', '9720.q1', '9720.br1', '9720.bs1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1215, 'diagramx': None, 'generators': [87261753600, 83548555, 456053154955, 693], 'label': '77760.bo.4860.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.bg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.bg1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056496
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1620.dh1', '1620.ei1', '2430.k1', '2430.l1', '2430.n1'], 'contains': ['9720.o1', '9720.q1', '9720.ca1', '9720.cb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1215, 'diagramx': None, 'generators': [87182277597, 355938191305, 317252, 374659402052], 'label': '77760.bo.4860.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.bh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.bh1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056497
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.dj1', '1620.dk1', '1620.dl1', '1620.ej1', '2430.h1', '2430.o1', '2430.q1'], 'contains': ['9720.n1', '9720.s1', '9720.t1', '9720.bl1', '9720.cd1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [443120025600, 178680, 180667244280, 442641109705], 'label': '77760.bo.4860.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.bi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.bi1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056498
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.di1', '1620.dm1', '1620.ek1', '2430.j1', '2430.m1', '2430.q1'], 'contains': ['9720.n1', '9720.n2', '9720.t1', '9720.bq1', '9720.ce1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [461841004800, 19678982400, 462320046985, 143304], 'label': '77760.bo.4860.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '4860.bj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.bj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056499
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.dn1', '1620.do1', '1620.dp1', '1620.el1', '2430.k1', '2430.m1', '2430.o1'], 'contains': ['9720.o1', '9720.r1', '9720.t1', '9720.bz1', '9720.ch1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [355938191405, 362615, 87182282615, 374659447415], 'label': '77760.bo.4860.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.bk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.bk1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056500
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.co2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1620.dq1', '1620.dr1', '1620.em1', '1620.en1', '2430.k1', '2430.p1', '2430.q1'], 'contains': ['9720.q1', '9720.t1', '9720.cc1', '9720.ci1', '9720.cj1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [362615, 355938105600, 87182282615, 374659447415], 'label': '77760.bo.4860.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '4860.bl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.bl1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056501
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.eo1', '1620.es1', '1620.ev1', '2430.a1', '2430.d1', '2430.o1'], 'contains': ['9720.v1', '9720.x1', '9720.bd1', '9720.bi1', '9720.bl1', '9720.bt1', '9720.bz1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [461841322052, 19678982400, 448908284158, 462320006400], 'label': '77760.bo.4860.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.bm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.bm1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056502
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.bm2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.ep1', '1620.es2', '1620.eu1', '2430.b1', '2430.c1', '2430.o1'], 'contains': ['9720.w1', '9720.x2', '9720.z1', '9720.bh2', '9720.bl1', '9720.bx1', '9720.bz1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [462320230584, 19678982400, 448908001949, 461841228984], 'label': '77760.bo.4860.bm2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.bm2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.bm2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056503
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.eq1', '1620.et1', '1620.ew1', '2430.b1', '2430.d1', '2430.n1'], 'contains': ['9720.v2', '9720.y1', '9720.z1', '9720.bh1', '9720.bo1', '9720.bt1', '9720.cb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [19678982400, 461841327358, 448908243571, 462320328958], 'label': '77760.bo.4860.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.bn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.bn1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056504
    {'ambient': '77760.bo', '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': '77760.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['20.a1', '20.b1', '20.c1', '20.d1', '20.e1', '20.f1', '20.g1', '20.h1', '30.e1', '90.w1'], 'core': '720.a1', 'coset_action_label': None, 'count': 10, 'diagramx': None, 'generators': [180587277504, 456053074316, 93449001331, 83543730, 143975, 174400173363, 85805, 80880, 80787, 143304], 'label': '77760.bo.10.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '10.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.a1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246056505
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.c1', '36.c1', '36.g1', '54.e1'], 'contains': ['216.e1', '216.p1', '216.t1', '324.a1', '540.w1', '648.d1', '1080.u1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [443555486666, 85805, 479001600, 80787], 'label': '77760.bo.108.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '108.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 246056506
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.ex1', '1620.ey1', '1620.fa1', '2430.c1', '2430.d1', '2430.m1'], 'contains': ['9720.v2', '9720.w1', '9720.ba1', '9720.bk1', '9720.bp1', '9720.bq1', '9720.bz1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [19678982400, 462320011709, 448908284158, 461841010109], 'label': '77760.bo.4860.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.bo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.bo1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056507
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.ck2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.er1', '1620.fb1', '1620.fd1', '2430.a1', '2430.e1', '2430.l1'], 'contains': ['9720.v1', '9720.bb1', '9720.bj1', '9720.br1', '9720.ca1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [19678982400, 461841327358, 448908284158, 462320006400], 'label': '77760.bo.4860.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '4860.bp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.bp1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056508
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.ez1', '1620.fc1', '2430.d1', '2430.l1'], 'contains': ['9720.v1', '9720.bc1', '9720.bk1', '9720.bs1', '9720.cb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [461841188645, 19678982400, 448908001949, 462320006400], 'label': '77760.bo.4860.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.bq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.bq1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056509
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.co2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1620.fe1', '1620.ff1', '1620.fg1', '2430.a1', '2430.p1'], 'contains': ['9720.x1', '9720.bb1', '9720.bu1', '9720.by1', '9720.cc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [461841286771, 19678982400, 448908243571, 462320006400], 'label': '77760.bo.4860.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '4860.br1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.br1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056510
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.ck2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.fh1', '1620.fi1', '1620.fj1', '1620.gf1', '2430.b1', '2430.e1', '2430.m1'], 'contains': ['9720.v2', '9720.w1', '9720.be1', '9720.bj1', '9720.bm1', '9720.ce1', '9720.ch1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [19678982400, 448908001949, 461841045149, 462320046749], 'label': '77760.bo.4860.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '4860.bs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.bs1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056511
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.co2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.fk1', '1620.fl1', '1620.fm1', '1620.gg1', '2430.b1', '2430.p1'], 'contains': ['9720.x2', '9720.y1', '9720.be1', '9720.bu1', '9720.bv1', '9720.cg1', '9720.ci1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [462320288371, 461841286771, 19678982400, 448908243571], 'label': '77760.bo.4860.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '4860.bt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.bt1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056512
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.ck2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.fn1', '1620.fo1', '1620.fp1', '2430.c1', '2430.e1', '2430.n1'], 'contains': ['9720.v2', '9720.z1', '9720.bf1', '9720.bn1', '9720.ca1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [462320092105, 461841090505, 19678982400, 448907961600], 'label': '77760.bo.4860.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '4860.bu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.bu1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056513
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.co2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1620.fq1', '1620.fr1', '1620.fs1', '2430.c1', '2430.p1'], 'contains': ['9720.x2', '9720.ba1', '9720.bf1', '9720.bw1', '9720.cc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [461841183480, 19678982400, 448907961600, 462320185080], 'label': '77760.bo.4860.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '4860.bv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.bv1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056514
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.ck2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.ft1', '1620.fu1', '1620.fv1', '1620.fw1', '1620.fx1', '1620.fy1', '2430.d1', '2430.e1', '2430.o1'], 'contains': ['9720.v1', '9720.w1', '9720.z1', '9720.bd1', '9720.bg1', '9720.cd1', '9720.ch1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841004800, 19678982400, 448908001949, 462320006400], 'label': '77760.bo.4860.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '4860.bw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.bw1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056515
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.co2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.fz1', '1620.ga1', '1620.gb1', '1620.gc1', '1620.gd1', '1620.ge1', '2430.d1', '2430.p1'], 'contains': ['9720.x1', '9720.y1', '9720.ba1', '9720.bc1', '9720.bg1', '9720.cf1', '9720.ci1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [461841004800, 19678982400, 448908243571, 462320006400], 'label': '77760.bo.4860.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '4860.bx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.bx1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056516
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.d1', '36.g1', '54.d1'], 'contains': ['216.f1', '216.q1', '216.u1', '324.a1', '540.x1', '648.f1', '1080.v1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [443555486666, 479047104, 5066, 80880], 'label': '77760.bo.108.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '108.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.f1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 246056517
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.bv2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1620.gh1', '1620.gi1', '1620.gj1', '1620.gk1', '2430.e1', '2430.p1'], 'contains': ['9720.bb1', '9720.be1', '9720.bf1', '9720.bg1', '9720.cj1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [461841004800, 19678982400, 448907961600, 462320006400], 'label': '77760.bo.4860.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '4860.by1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.by1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056518
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.gl1', '1620.gn1', '1620.go1', '2430.a1', '2430.f1', '2430.n1'], 'contains': ['9720.bh1', '9720.bn1', '9720.bt1', '9720.by1', '9720.ca1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [19678982400, 461841327358, 462320092346, 448908243571], 'label': '77760.bo.4860.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.bz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.bz1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056519
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.gp1', '1620.gq1', '1620.gt1', '2430.a1', '2430.b1', '2430.m1'], 'contains': ['9720.bh1', '9720.bi1', '9720.bj1', '9720.bm1', '9720.bq1', '9720.bu1', '9720.bz1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [19678982400, 461841327358, 448908284158, 462320046985], 'label': '77760.bo.4860.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.ca1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.ca1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056520
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.gr1', '1620.gu1', '2430.b1', '2430.l1'], 'contains': ['9720.bh2', '9720.bj1', '9720.bs1', '9720.bv1', '9720.cb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [19678982400, 461841327358, 448908284158, 462320369015], 'label': '77760.bo.4860.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.cb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.cb1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056521
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.gm1', '1620.gv1', '1620.gw1', '2430.c1', '2430.f1', '2430.l1'], 'contains': ['9720.bh2', '9720.bk1', '9720.br1', '9720.bw1', '9720.ca1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [462320230584, 461841188645, 19678982400, 448908001949], 'label': '77760.bo.4860.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.cc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.cc1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056522
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.gs1', '1620.gx1', '1620.gy1', '2430.a1', '2430.c1', '2430.q1'], 'contains': ['9720.bl1', '9720.bn1', '9720.bq1', '9720.br1', '9720.cc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [461841322052, 19678982400, 462320011709, 448908284158], 'label': '77760.bo.4860.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.cd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.cd1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056523
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.gz1', '1620.hd1', '1620.he1', '1620.hf1', '1620.hg1', '2430.b1', '2430.f1', '2430.o1'], 'contains': ['9720.bh2', '9720.bi1', '9720.bt1', '9720.bx1', '9720.cd1', '9720.cg1', '9720.ch1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [461841004800, 19678982400, 448908284158, 462320369015], 'label': '77760.bo.4860.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.ce1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.ce1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056524
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.ha1', '1620.hb1', '1620.hc1', '1620.hk1', '1620.hl1', '2430.d1', '2430.f1', '2430.m1'], 'contains': ['9720.bh1', '9720.bi1', '9720.bk1', '9720.bp1', '9720.ce1', '9720.cf1', '9720.ch1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [461841188645, 19678982400, 448908001949, 462320046749], 'label': '77760.bo.4860.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.cf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.cf1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056525
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.hh1', '1620.hi1', '1620.hj1', '1620.hm1', '1620.hn1', '2430.b1', '2430.d1', '2430.q1'], 'contains': ['9720.bl1', '9720.bo1', '9720.bq1', '9720.bs1', '9720.cd1', '9720.ce1', '9720.ci1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [19678982400, 448908001949, 461841228984, 462320046749], 'label': '77760.bo.4860.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '4860.cg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.cg1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056526
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.ck2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.ho1', '1620.hp1', '1620.hq1', '1620.hu1', '2430.e1', '2430.f1', '2430.q1'], 'contains': ['9720.bn1', '9720.br1', '9720.cd1', '9720.ce1', '9720.cj1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [461841004800, 19678982400, 448908001949, 462320046749], 'label': '77760.bo.4860.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '4860.ch1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.ch1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056527
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.e1', '36.h1', '54.d1'], 'contains': ['216.f1', '216.s1', '216.w1', '324.b1', '540.be1', '648.g1', '1080.bc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [479283571, 183845, 224515, 443555838962], 'label': '77760.bo.108.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '108.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.g1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 246056528
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4860.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.co2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1620.hr1', '1620.hs1', '1620.ht1', '1620.hv1', '2430.f1', '2430.p1'], 'contains': ['9720.bw1', '9720.by1', '9720.cf1', '9720.cg1', '9720.cj1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [461841004800, 462320288371, 19678982400, 448908243571], 'label': '77760.bo.4860.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '4860.ci1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4860.ci1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056529
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '5184.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.a1', '1728.b1', '2592.b1', '2592.d1', '2592.g1', '2592.k1', '2592.m1'], 'contains': ['15552.a1', '25920.a1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18764605587, 80787], 'label': '77760.bo.5184.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '5184.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 246056530
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '5184.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.a1', '2592.a1', '2592.c1', '2592.e1', '2592.h1', '2592.j1', '2592.l1', '2592.n1'], 'contains': ['15552.a1', '25920.b1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [18764605680, 80880], 'label': '77760.bo.5184.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '5184.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.b1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 246056532
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '270.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.a1', '2160.b1', '2160.o1', '3240.a1', '3240.a2', '3240.d1', '3240.d2', '3240.bl1'], 'contains': ['12960.a1', '12960.l1', '12960.w1', '19440.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [442641386187, 143975, 85805], 'label': '77760.bo.6480.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '6480.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056533
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.bi1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.i1', '2160.a1', '2160.d1', '2160.p1', '2160.r1', '3240.b1', '3240.f1', '3240.q1'], 'contains': ['12960.b1', '12960.n1', '12960.x1', '19440.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [183845, 518918400, 442641024000], 'label': '77760.bo.6480.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '6480.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056534
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.j1', '2160.a1', '2160.c1', '2160.q1', '3240.c1'], 'contains': ['12960.c1', '12960.p1', '12960.y1', '19440.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [519280587, 442641024000, 85805], 'label': '77760.bo.6480.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.a1', 'old_label': '6480.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056535
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.bj1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.k1', '2160.b1', '2160.c1', '2160.d1', '2160.s1', '2160.t1', '3240.e1', '3240.f1', '3240.r1'], 'contains': ['12960.b1', '12960.r1', '12960.bb1', '19440.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [188331091200, 85805, 375138172205], 'label': '77760.bo.6480.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '6480.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056536
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.a1', '2160.e1', '2160.u1', '3240.d1', '3240.d2', '3240.g1', '3240.g2', '3240.h1', '3240.i1', '3240.j1', '3240.k1', '3240.l1', '3240.n1', '3240.bm1'], 'contains': ['12960.a1', '12960.t1', '12960.bm1', '19440.b1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [183845, 274467997680, 80880], 'label': '77760.bo.6480.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '6480.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056537
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.c1', '1620.z1', '2160.e1', '2160.f1', '2160.v1', '2160.w1', '3240.f1', '3240.m1', '3240.s1'], 'contains': ['12960.b1', '12960.v1', '12960.bp1', '19440.b1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [113566924800, 88176252092, 40892], 'label': '77760.bo.6480.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '6480.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056538
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.f1', '36.d1', '36.h1', '54.e1'], 'contains': ['216.e1', '216.t1', '216.v1', '324.b1', '540.bh1', '648.e1', '1080.bd1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [174879492215, 277050, 80787, 462320046985], 'label': '77760.bo.108.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '108.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 246056539
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.q1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.q1', '2160.g1', '2160.h1', '2160.i1', '2160.x1', '2160.y1', '3240.e1', '3240.m1', '3240.q1'], 'contains': ['12960.b1', '12960.x1', '12960.bf1', '19440.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 6480, 'diagramx': None, 'generators': [174436554242, 138242, 375138091466], 'label': '77760.bo.6480.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1620.ba1', 'old_label': '6480.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056540
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.g1', '2160.j1', '2160.ba1', '3240.a1', '3240.a2', '3240.g1', '3240.g2', '3240.bl1'], 'contains': ['12960.a1', '12960.ba1', '12960.bh1', '19440.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [277050, 45363, 442641341252], 'label': '77760.bo.6480.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '6480.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056541
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.s1', '2160.i1', '2160.j1', '2160.z1', '2160.bb1', '3240.b1', '3240.m1', '3240.r1'], 'contains': ['12960.b1', '12960.bb1', '12960.bj1', '19440.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [188331091200, 85805, 375138172555], 'label': '77760.bo.6480.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.j1', 'old_label': '6480.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.i1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056542
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.t1', '2160.h1', '2160.j1', '2160.bc1', '3240.c1'], 'contains': ['12960.c1', '12960.bd1', '12960.bk1', '19440.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [5309, 442162201412, 442641341252], 'label': '77760.bo.6480.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.c1', 'old_label': '6480.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.j1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056543
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.b1', '2160.k1', '2160.be1', '3240.a1', '3240.a2', '3240.l1', '3240.bm1'], 'contains': ['12960.a1', '12960.bo1', '12960.bt1', '19440.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [179012, 5309, 274468095480], 'label': '77760.bo.6480.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '6480.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.k1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056544
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.w1', '2160.k1', '2160.l1', '2160.m1', '2160.bd1', '2160.bf1', '3240.b1', '3240.e1', '3240.s1'], 'contains': ['12960.b1', '12960.bp1', '12960.bv1', '19440.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 6480, 'diagramx': None, 'generators': [442637395200, 40585, 368392188092], 'label': '77760.bo.6480.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1620.ba1', 'old_label': '6480.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.l1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056545
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.x1', '2160.k1', '2160.l1', '2160.bg1', '3240.c1'], 'contains': ['12960.c1', '12960.br1', '12960.bw1', '19440.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 12960, 'diagramx': None, 'generators': [442637757387, 40585, 368392188092], 'label': '77760.bo.6480.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3240.c1', 'old_label': '6480.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.m1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056546
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.bb1', '2160.n1', '2160.bh1', '2160.bi1', '3240.q1', '3240.r1', '3240.s1'], 'contains': ['12960.b1', '12960.g1', '19440.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [355419504452, 5309, 317252], 'label': '77760.bo.6480.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.j1', 'old_label': '6480.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056547
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '270.by1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.o1', '2160.p1', '2160.q1', '2160.s1', '2160.bj1', '3240.u1', '3240.u2', '3240.v1', '3240.v2', '3240.bn1'], 'contains': ['12960.d1', '12960.k1', '12960.z1', '19440.a1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [183845, 442641024000, 80787], 'label': '77760.bo.6480.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '6480.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.o1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056548
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.r1', '2160.t1', '2160.bj1', '3240.t1', '3240.t2', '3240.w1', '3240.w2', '3240.bl1'], 'contains': ['12960.e1', '12960.l1', '12960.ba1', '19440.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [442641104880, 85805, 80880], 'label': '77760.bo.6480.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '6480.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.p1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056549
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.g1', '36.i1', '54.d1'], 'contains': ['216.b1', '216.f1', '216.n1', '324.c1', '540.bs1', '648.h1', '1080.bk1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [143975, 286483093054, 40585, 25470766654, 143304], 'label': '77760.bo.108.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '108.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.i1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 246056550
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.c1', '2160.u1', '2160.v1', '2160.bk1', '3240.v1', '3240.v2', '3240.y1', '3240.y2', '3240.z1', '3240.ba1', '3240.bb1', '3240.bc1', '3240.bi1', '3240.bj1', '3240.bo1'], 'contains': ['12960.d1', '12960.s1', '12960.bn1', '19440.b1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [183845, 274467962404, 80787], 'label': '77760.bo.6480.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '6480.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.q1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056551
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.d1', '2160.w1', '2160.bk1', '3240.w1', '3240.w2', '3240.x1', '3240.x2', '3240.bd1', '3240.be1', '3240.bf1', '3240.bg1', '3240.bh1', '3240.bk1', '3240.bm1'], 'contains': ['12960.e1', '12960.t1', '12960.bo1', '19440.b1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [274467997680, 85805, 80880], 'label': '77760.bo.6480.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '6480.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.r1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056552
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.x1', '2160.z1', '2160.bl1', '3240.t1', '3240.t2', '3240.x1', '3240.x2', '3240.bl1'], 'contains': ['12960.e1', '12960.w1', '12960.bh1', '19440.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [45363, 442641341252, 85805], 'label': '77760.bo.6480.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '6480.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.s1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056553
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bs1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.y1', '2160.ba1', '2160.bb1', '2160.bc1', '2160.bl1', '3240.u1', '3240.u2', '3240.y1', '3240.y2', '3240.bn1'], 'contains': ['12960.d1', '12960.z1', '12960.be1', '19440.c1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [442641386755, 5309, 80787], 'label': '77760.bo.6480.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '6480.t1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.t1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056554
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.e1', '2160.bd1', '2160.bm1', '3240.t1', '3240.t2', '3240.bh1', '3240.bm1'], 'contains': ['12960.e1', '12960.bm1', '12960.bt1', '19440.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [85805, 80880, 274468095480], 'label': '77760.bo.6480.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '6480.u1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.u1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056555
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.f1', '2160.be1', '2160.bf1', '2160.bg1', '2160.bm1', '3240.u1', '3240.u2', '3240.bi1', '3240.bo1'], 'contains': ['12960.d1', '12960.bn1', '12960.bs1', '19440.d1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [274468060348, 5309, 80787], 'label': '77760.bo.6480.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '6480.v1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.v1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056556
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.g1', '2160.bh1', '2160.bn1', '3240.bl1', '3240.bm1'], 'contains': ['12960.a1', '12960.e1', '12960.i1', '19440.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [85805, 80880, 143304], 'label': '77760.bo.6480.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '720.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '6480.w1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.w1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056557
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.h1', '2160.bi1', '2160.bn1', '3240.bn1', '3240.bo1'], 'contains': ['12960.d1', '12960.f1', '19440.e1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [85805, 80787, 143304], 'label': '77760.bo.6480.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '720.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '6480.x1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.x1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056558
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '270.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.bo1', '2160.bp1', '2160.cb1', '2160.cc1', '3240.bn1', '3240.bp1', '3240.bp2', '3240.bs1', '3240.bs2'], 'contains': ['12960.f1', '12960.k1', '12960.be1', '19440.f1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [442641024000, 80787, 143304], 'label': '77760.bo.6480.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '6480.y1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.y1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056559
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.bl1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.da1', '2160.bo1', '2160.br1', '2160.cd1', '2160.cf1', '3240.q1', '3240.bq1', '3240.bu1'], 'contains': ['12960.g1', '12960.n1', '12960.bf1', '19440.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [224184, 174436640184, 375138086400], 'label': '77760.bo.6480.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '6480.z1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.z1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056560
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.h1', '36.i1', '54.e1'], 'contains': ['216.e1', '216.j1', '324.c1', '540.bu1', '648.i1', '1080.bn1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [286482914185, 85805, 25470587785, 80787, 143304], 'label': '77760.bo.108.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '108.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.j1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 246056561
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.bo1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.db1', '2160.bo1', '2160.bq1', '2160.ce1', '2160.cg1', '3240.br1'], 'contains': ['12960.h1', '12960.o1', '12960.bg1', '19440.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [224184, 174436559403, 375138086400], 'label': '77760.bo.6480.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.bz1', 'old_label': '6480.ba1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.ba1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056562
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.bm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.dc1', '2160.bp1', '2160.bq1', '2160.br1', '2160.ch1', '2160.ci1', '3240.r1', '3240.bt1', '3240.bu1'], 'contains': ['12960.g1', '12960.r1', '12960.bj1', '19440.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [188331269880, 178680, 375138086400], 'label': '77760.bo.6480.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.r1', 'old_label': '6480.bb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.bb1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056563
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.i1', '2160.bs1', '2160.cj1', '2160.ck1', '3240.bo1', '3240.bs1', '3240.bs2', '3240.bv1', '3240.bv2', '3240.bw1', '3240.bx1', '3240.by1', '3240.bz1', '3240.ca1', '3240.cc1'], 'contains': ['12960.f1', '12960.s1', '12960.bs1', '19440.g1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [274467962404, 80787, 143304], 'label': '77760.bo.6480.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '6480.bc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.bc1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056564
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.l1', '1620.dr1', '2160.bs1', '2160.bt1', '2160.cl1', '2160.cm1', '3240.s1', '3240.bu1', '3240.cb1'], 'contains': ['12960.g1', '12960.v1', '12960.bv1', '19440.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [450, 442637395200, 368392147650], 'label': '77760.bo.6480.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '6480.bd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.bd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056565
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.di1', '2160.bu1', '2160.bv1', '2160.bw1', '2160.cn1', '3240.q1', '3240.bt1', '3240.cb1'], 'contains': ['12960.g1', '12960.x1', '19440.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [178680, 518918400, 442641109705], 'label': '77760.bo.6480.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1620.ba1', 'old_label': '6480.be1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.be1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056566
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.bu1', '2160.bx1', '2160.co1', '3240.bn1', '3240.bp1', '3240.bp2', '3240.bv1', '3240.bv2'], 'contains': ['12960.f1', '12960.z1', '19440.h1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [178680, 442641109705, 80787], 'label': '77760.bo.6480.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '6480.bf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.bf1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056567
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.dk1', '2160.bw1', '2160.bx1', '2160.cp1', '3240.r1', '3240.bq1', '3240.cb1'], 'contains': ['12960.g1', '12960.bb1', '19440.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [178680, 442162022400, 442641109705], 'label': '77760.bo.6480.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.j1', 'old_label': '6480.bg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.bg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056568
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.dl1', '2160.bv1', '2160.bx1', '2160.cq1', '3240.br1'], 'contains': ['12960.h1', '12960.bc1', '19440.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [188331270027, 375138172205, 143304], 'label': '77760.bo.6480.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.cb1', 'old_label': '6480.bh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.bh1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056569
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.j1', '2160.by1', '2160.cr1', '3240.bo1', '3240.bp1', '3240.bp2', '3240.bw1'], 'contains': ['12960.f1', '12960.bn1', '19440.i1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [178680, 274468002505, 80787], 'label': '77760.bo.6480.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '6480.bi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.bi1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056570
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.do1', '2160.by1', '2160.bz1', '2160.ca1', '2160.cs1', '3240.s1', '3240.bq1', '3240.bt1'], 'contains': ['12960.g1', '12960.bp1', '19440.i1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [113566924800, 88176252092, 693], 'label': '77760.bo.6480.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1620.ba1', 'old_label': '6480.bj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.bj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056571
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.i1', '36.j1'], 'contains': ['216.c1', '216.d1', '216.g1', '216.h1', '216.i1', '216.k1', '216.l1', '324.d1', '324.e1', '540.cn1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [80787, 269202533759, 267841769035, 85805, 181146153355, 80880, 693], 'label': '77760.bo.108.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '108.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 246056572
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.dp1', '2160.by1', '2160.bz1', '2160.ct1', '3240.br1'], 'contains': ['12960.h1', '12960.bq1', '19440.i1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 6480, 'diagramx': None, 'generators': [113567005587, 88176252092, 693], 'label': '77760.bo.6480.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3240.br1', 'old_label': '6480.bk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.bk1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056573
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '270.p1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.cb1', '2160.cd1', '2160.ce1', '2160.ch1', '3240.bl1', '3240.cf1', '3240.cf2', '3240.cg1', '3240.cg2'], 'contains': ['12960.i1', '12960.l1', '12960.bh1', '19440.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [442641104880, 80880, 143304], 'label': '77760.bo.6480.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '6480.bl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.bl1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056574
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.ga1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.cc1', '2160.cf1', '2160.cg1', '2160.ci1', '3240.ch1', '3240.ch2'], 'contains': ['12960.j1', '12960.m1', '12960.bi1', '19440.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [442641305544, 143731, 143304], 'label': '77760.bo.6480.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '6480.bm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.bm1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056575
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.k1', '2160.cj1', '2160.cl1', '3240.bm1', '3240.cg1', '3240.cg2', '3240.ci1', '3240.ci2', '3240.cj1', '3240.ck1', '3240.cl1', '3240.cm1', '3240.cn1', '3240.cq1'], 'contains': ['12960.i1', '12960.t1', '12960.bt1', '19440.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [274467916800, 143975, 143304], 'label': '77760.bo.6480.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '6480.bn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.bn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056576
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.l1', '2160.ck1', '2160.cm1', '3240.ch1', '3240.ch2', '3240.co1', '3240.cp1', '3240.cr1'], 'contains': ['12960.j1', '12960.u1', '12960.bu1', '19440.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [274467916800, 143731, 143304], 'label': '77760.bo.6480.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '6480.bo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.bo1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056577
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.cn1', '2160.co1', '2160.cp1', '2160.cq1', '3240.bl1', '3240.cf1', '3240.cf2', '3240.ci1', '3240.ci2'], 'contains': ['12960.i1', '12960.w1', '12960.ba1', '19440.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [179012, 178680, 442641300482], 'label': '77760.bo.6480.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '6480.bp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.bp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056578
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.m1', '2160.cr1', '2160.cs1', '2160.ct1', '3240.bm1', '3240.cf1', '3240.cf2', '3240.cj1'], 'contains': ['12960.i1', '12960.bm1', '12960.bo1', '19440.i1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [179012, 178680, 274468002505], 'label': '77760.bo.6480.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '6480.bq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.bq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056579
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.cu1', '2160.cv1', '2160.cw1', '2160.dl1', '3240.d1', '3240.t1', '3240.cf1', '3240.cs2', '3240.cs4', '3240.cu1', '3240.cu2'], 'contains': ['12960.l1', '12960.w1', '12960.bm1', '19440.j1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [87182196721, 143975, 375138270474], 'label': '77760.bo.6480.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bd1', 'old_label': '6480.br1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.br1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056580
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.br2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.cu2', '3240.d2', '3240.t2', '3240.cf2', '3240.cs1', '3240.cs3', '3240.cu1', '3240.cu2'], 'contains': ['12960.l1', '12960.w1', '12960.bm1', '19440.j2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [448908283441, 224515, 442641305788], 'label': '77760.bo.6480.br2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '6480.br2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.br2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056581
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.ec1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.cu1', '2160.cx1', '2160.cy1', '2160.cz1', '2160.dm1', '3240.u1', '3240.v1', '3240.bp1', '3240.ct1', '3240.ct3', '3240.cw1', '3240.cw2'], 'contains': ['12960.k1', '12960.z1', '12960.bn1', '19440.j1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [87181925066, 375138172205, 80787], 'label': '77760.bo.6480.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bj1', 'old_label': '6480.bs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.bs1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056582
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '108.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.j1', '36.l1', '36.m1', '54.e1'], 'contains': ['216.j1', '216.p1', '216.v1', '324.f1', '540.cr1', '648.j1', '1080.cd1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [362615, 443555763716, 479001600, 80787], 'label': '77760.bo.108.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '108.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.l1', 'subgroup_fusion': None, 'weyl_group': '240.189'}
  • id: 246056583
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.bs2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bz1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.cu2', '2160.cx2', '3240.u2', '3240.v2', '3240.bp2', '3240.ct1', '3240.ct2', '3240.cw1', '3240.cw2'], 'contains': ['12960.k1', '12960.z1', '12960.bn1', '19440.j2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [448908007204, 442641301050, 80787], 'label': '77760.bo.6480.bs2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '6480.bs2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.bs2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056584
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.cx1', '2160.da1', '2160.db1', '2160.dn1', '3240.a1', '3240.w1', '3240.cf1', '3240.cs1', '3240.cs4', '3240.cx1', '3240.cx2'], 'contains': ['12960.l1', '12960.ba1', '12960.bo1', '19440.j1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [375138172205, 80880, 87182005805], 'label': '77760.bo.6480.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bd1', 'old_label': '6480.bt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.bt1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056585
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.bt2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.cx2', '3240.a2', '3240.w2', '3240.cf2', '3240.cs2', '3240.cs3', '3240.cx1', '3240.cx2'], 'contains': ['12960.l1', '12960.ba1', '12960.bo1', '19440.j2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [442641024148, 448908001949, 148], 'label': '77760.bo.6480.bt2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '6480.bt2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.bt2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056586
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.fw1', '2160.cv1', '2160.cy1', '2160.da1', '2160.dq1', '3240.b1', '3240.f1', '3240.bq1'], 'contains': ['12960.n1', '12960.bb1', '12960.bp1', '19440.j1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [368871234955, 174436416000, 375138086400], 'label': '77760.bo.6480.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '6480.bu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.bu1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056587
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.fx1', '2160.cw1', '2160.cy1', '2160.db1', '2160.do1', '3240.br1'], 'contains': ['12960.o1', '12960.bc1', '12960.bq1', '19440.j1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [174436496787, 368871153961, 375138086400], 'label': '77760.bo.6480.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.cm1', 'old_label': '6480.bv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.bv1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056588
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.fy1', '2160.cz1', '2160.da1', '2160.db1', '2160.dp1', '3240.c1'], 'contains': ['12960.p1', '12960.bd1', '12960.br1', '19440.j1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 12960, 'diagramx': None, 'generators': [368871153961, 174436416243, 375138086400], 'label': '77760.bo.6480.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3240.c1', 'old_label': '6480.bw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.bw1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056589
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.cz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.dc1', '2160.dd1', '2160.de1', '2160.df1', '2160.dg1', '2160.dr1', '3240.u1', '3240.bs1', '3240.ct1', '3240.da1', '3240.da2'], 'contains': ['12960.k1', '12960.be1', '12960.bs1', '19440.k1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [442641024000, 443120071554, 80787], 'label': '77760.bo.6480.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bi1', 'old_label': '6480.bx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.bx1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056590
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.bx2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.br1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.dc2', '2160.dd2', '3240.u2', '3240.bs2', '3240.ct2', '3240.ct3', '3240.da1', '3240.da2'], 'contains': ['12960.k1', '12960.be1', '12960.bs1', '19440.k2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [448908278999, 442641024000, 80787], 'label': '77760.bo.6480.bx2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '6480.bx2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.bx2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056785
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.p1', '4320.b1', '4320.c1', '4320.g1', '6480.c1', '6480.j1', '6480.m1'], 'contains': ['25920.f1', '38880.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [183845, 194518240704], 'label': '77760.bo.12960.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.a1', 'old_label': '12960.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056591
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.bq1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.dc1', '2160.dh1', '2160.ds1', '3240.a1', '3240.t1', '3240.cg1', '3240.cs1', '3240.cs2', '3240.dc1', '3240.dc2'], 'contains': ['12960.l1', '12960.bh1', '12960.bt1', '19440.k1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [45363, 87182282615, 375138086400], 'label': '77760.bo.6480.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bj1', 'old_label': '6480.by1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.by1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056592
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.by2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.w1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.dc2', '3240.a2', '3240.t2', '3240.cg2', '3240.cs3', '3240.cs4', '3240.dc1', '3240.dc2'], 'contains': ['12960.l1', '12960.bh1', '12960.bt1', '19440.k2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [448908042244, 45363, 442641341252], 'label': '77760.bo.6480.by2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '6480.by2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.by2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056593
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.k1', '36.n1', '54.e1'], 'contains': ['216.j1', '216.t1', '324.g1', '540.cv1', '648.k1', '1080.cf1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [317399, 443555839197, 479087546, 80787], 'label': '77760.bo.108.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '108.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 246056594
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.dd1', '2160.di1', '2160.dt1', '3240.ch1', '3240.dd1', '3240.dd2'], 'contains': ['12960.m1', '12960.bi1', '12960.bu1', '19440.k1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [375138265559, 87182282615, 179159], 'label': '77760.bo.6480.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.dk1', 'old_label': '6480.bz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.bz1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056595
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.bz2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.dd2', '3240.ch2', '3240.dd1', '3240.dd2'], 'contains': ['12960.m1', '12960.bi1', '12960.bu1', '19440.k2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [442641341252, 448908278667, 224612], 'label': '77760.bo.6480.bz2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '6480.bz2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.bz2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056596
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.gc1', '2160.de1', '2160.dh1', '2160.di1', '2160.dw1', '3240.b1', '3240.bu1'], 'contains': ['12960.n1', '12960.bj1', '12960.bv1', '19440.k1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [368871149398, 174436416000, 375138086400], 'label': '77760.bo.6480.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '6480.ca1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.ca1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056597
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.gd1', '2160.df1', '2160.dh1', '2160.du1', '3240.c1'], 'contains': ['12960.p1', '12960.bk1', '12960.bw1', '19440.k1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [368871149398, 174436416243, 375138086400], 'label': '77760.bo.6480.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.q1', 'old_label': '6480.cb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.cb1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056598
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.ge1', '2160.dg1', '2160.di1', '2160.dv1'], 'contains': ['12960.q1', '12960.bl1', '12960.bx1', '19440.k1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [997920598, 442641024000, 519235228], 'label': '77760.bo.6480.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2160.dg1', 'old_label': '6480.cc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.cc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056599
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.cw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.dj1', '2160.dk1', '2160.dx1', '3240.v1', '3240.bs1', '3240.cw2', '3240.cy1', '3240.da2', '3240.db1', '3240.dh1', '3240.dj1', '3240.dv1', '3240.dy1', '3240.eb1'], 'contains': ['12960.k1', '12960.s1', '19440.l1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [80787, 375138086400, 87182000787], 'label': '77760.bo.6480.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '6480.cd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.cd1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056600
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.cd2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '90.bi1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.dj2', '2160.dk2', '3240.v2', '3240.bs2', '3240.cw1', '3240.da1', '3240.dm1', '3240.dn1', '3240.do1', '3240.eb1'], 'contains': ['12960.k1', '12960.s1', '19440.l2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [448908007204, 442641024000, 80787], 'label': '77760.bo.6480.cd2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '6480.cd2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.cd2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056601
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.s1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.dj1', '2160.dy1', '3240.d1', '3240.w1', '3240.cg1', '3240.cu2', '3240.cv1', '3240.cx2', '3240.cz1', '3240.dc2', '3240.de1', '3240.dg1', '3240.di1', '3240.dk1', '3240.dw1', '3240.dz1', '3240.ec1'], 'contains': ['12960.l1', '12960.t1', '19440.l1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [143975, 375138230375, 87182282187], 'label': '77760.bo.6480.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '6480.ce1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.ce1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056602
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.ce2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '270.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.dj2', '3240.d2', '3240.w2', '3240.cg2', '3240.cu1', '3240.cx1', '3240.dc1', '3240.dp1', '3240.dq1', '3240.dr1', '3240.ds1', '3240.ec1'], 'contains': ['12960.l1', '12960.t1', '19440.l2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [442641386187, 143975, 448908323787], 'label': '77760.bo.6480.ce2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '6480.ce2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.ce2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056603
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.ef1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.dk1', '2160.dz1', '3240.ch1', '3240.dd2', '3240.df1', '3240.dl1', '3240.dx1', '3240.ea1', '3240.ed1'], 'contains': ['12960.m1', '12960.u1', '19440.l1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [375138265559, 87182282284, 179159], 'label': '77760.bo.6480.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '6480.cf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.cf1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056604
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '108.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1', '36.o1', '36.p1', '54.c1', '54.f1', '54.g1'], 'contains': ['216.a1', '648.l1', '1080.ci1', '1620.dr1'], 'core': '216.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [362615, 274511462400, 87182282615], 'label': '77760.bo.108.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '108.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.n1', 'subgroup_fusion': None, 'weyl_group': '720.763'}
  • id: 246056605
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.cf2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.fz1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.dk2', '3240.ch2', '3240.dd1', '3240.dt1', '3240.du1', '3240.ed1'], 'contains': ['12960.m1', '12960.u1', '19440.l2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [448908323884, 442641386284, 179159], 'label': '77760.bo.6480.cf2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '6480.cf2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.cf2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056606
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.gf1', '2160.dl1', '2160.dm1', '2160.dn1', '2160.do1', '2160.dp1', '2160.dq1', '3240.e1', '3240.f1', '3240.bt1'], 'contains': ['12960.r1', '12960.x1', '12960.bp1', '19440.j1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [518918400, 997920000, 442641301050], 'label': '77760.bo.6480.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '6480.cg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.cg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056607
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1620.gg1', '2160.dr1', '2160.ds1', '2160.dt1', '2160.du1', '2160.dv1', '2160.dw1', '3240.e1', '3240.bu1'], 'contains': ['12960.r1', '12960.bf1', '12960.bv1', '19440.k1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [375138087093, 368871148800, 174436416000], 'label': '77760.bo.6480.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '6480.ch1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.ch1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056608
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.bs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.p1', '1620.gk1', '2160.dx1', '2160.dy1', '2160.dz1', '2160.ea1', '3240.f1', '3240.bu1'], 'contains': ['12960.n1', '12960.r1', '12960.v1', '19440.l1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [368871148800, 174436416000, 375138086400], 'label': '77760.bo.6480.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '6480.ci1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.ci1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056609
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.eb1', '2160.ev1', '3240.d1', '3240.x1', '3240.ci1', '3240.cu1', '3240.cv1', '3240.ej2', '3240.ek1', '3240.el1', '3240.em1', '3240.en1', '3240.es1', '3240.fl2', '3240.fm1', '3240.gu1', '3240.gv1'], 'contains': ['12960.t1', '12960.w1', '19440.m1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [179012, 443120204612, 442641300482], 'label': '77760.bo.6480.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '6480.cj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.cj1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056627
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '108.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.m1', '36.m1'], 'contains': ['216.o1', '216.r1', '216.x1', '324.f1', '540.dq1', '648.o1', '1080.cr1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [462320287944, 174879411571, 143731, 143304], 'label': '77760.bo.108.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.m1', 'old_label': '108.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.p1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 246056610
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.cj2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.eb2', '3240.d2', '3240.x2', '3240.ci2', '3240.cu2', '3240.ej1', '3240.eo1', '3240.ep1', '3240.eq1', '3240.er1', '3240.fl1', '3240.gv1'], 'contains': ['12960.t1', '12960.w1', '19440.m2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [45363, 442641300958, 448908283914], 'label': '77760.bo.6480.cj2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '6480.cj2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.cj2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056611
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.ec1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.eb1', '2160.ec1', '2160.ew1', '3240.v1', '3240.y1', '3240.bv1', '3240.cw1', '3240.cy1', '3240.et2', '3240.eu1', '3240.ey1', '3240.ez1', '3240.fb1', '3240.fn1', '3240.fo1', '3240.fp1', '3240.gy1', '3240.hd1'], 'contains': ['12960.s1', '12960.z1', '19440.m1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [375138172555, 80787, 87182000787], 'label': '77760.bo.6480.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '6480.ck1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.ck1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056612
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.ck2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.eb2', '2160.ec2', '3240.v2', '3240.y2', '3240.bv2', '3240.cw2', '3240.et1', '3240.fd1', '3240.fe1', '3240.ff1', '3240.fg1', '3240.fn1', '3240.hd1'], 'contains': ['12960.s1', '12960.z1', '19440.m2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [448908284158, 442641301050, 80787], 'label': '77760.bo.6480.ck2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '6480.ck2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.ck2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056613
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.ec1', '2160.ex1', '3240.g1', '3240.w1', '3240.ci1', '3240.cx1', '3240.cz1', '3240.ev2', '3240.ew1', '3240.ex1', '3240.fa1', '3240.fc1', '3240.fl1', '3240.fm1', '3240.fq1', '3240.gz1', '3240.he1'], 'contains': ['12960.t1', '12960.ba1', '19440.m1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [443120025600, 442641109705, 80880], 'label': '77760.bo.6480.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '6480.cl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.cl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056614
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.cl2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.ec2', '3240.g2', '3240.w2', '3240.ci2', '3240.cx2', '3240.ev1', '3240.fh1', '3240.fi1', '3240.fj1', '3240.fk1', '3240.fl2', '3240.he1'], 'contains': ['12960.t1', '12960.ba1', '19440.m2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [442641346558, 143975, 448908284158], 'label': '77760.bo.6480.cl2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '6480.cl2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.cl2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056615
    {'ambient': '77760.bo', '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': '77760.a1', 'complements': ['6480.bp1', '6480.p1', '6480.s1', '6480.bl1', '6480.bm1', '6480.dw2', '6480.by2', '6480.bz2', '6480.ed2', '6480.bt2', '6480.by1', '6480.bz1', '6480.dw1', '6480.bt1', '6480.ed1', '6480.ef1', '6480.bw1', '6480.dy1', '6480.cb1', '6480.cc1'], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '6.a1', '6.d1', '6.e1'], 'contains': ['24.a1', '36.e1', '36.f1', '72.e1', '120.o1', '180.bs1'], 'core': '12.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [183845, 87182277597, 274511462400, 143975, 80787], 'label': '77760.bo.12.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': ['4.a1', '6.a1'], 'normal_contains': ['24.a1', '4320.a1'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '77760.bo', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '77760.bo'}
  • id: 246056616
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '108.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.l1', '36.l1', '54.d1'], 'contains': ['216.n1', '216.q1', '216.w1', '324.f1', '540.dp1', '648.m1', '1080.cq1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [362615, 45363, 443555844215, 479082244], 'label': '77760.bo.108.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '108.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.o1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 246056617
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.cz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.ed1', '2160.ee1', '2160.ey1', '3240.y1', '3240.bs1', '3240.da1', '3240.db1', '3240.et1', '3240.eu1', '3240.fr1', '3240.fs1', '3240.fw1', '3240.hf1', '3240.hg1'], 'contains': ['12960.s1', '12960.be1', '19440.n1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [375138087093, 80787, 87182000787], 'label': '77760.bo.6480.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '6480.cm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.cm1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056618
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.cm2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.ed2', '2160.ee2', '3240.y2', '3240.bs2', '3240.da2', '3240.et2', '3240.ft1', '3240.fu1', '3240.fv1', '3240.hg1'], 'contains': ['12960.s1', '12960.be1', '19440.n2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [448908278999, 442641386852, 80787], 'label': '77760.bo.6480.cm2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '6480.cm2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.cm2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056619
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.bq1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.ed1', '2160.ez1', '3240.g1', '3240.x1', '3240.cg1', '3240.dc1', '3240.de1', '3240.ej1', '3240.ek1', '3240.ev1', '3240.ew1', '3240.fx1', '3240.fy1', '3240.fz1', '3240.gh1', '3240.hj1', '3240.ho1'], 'contains': ['12960.t1', '12960.bh1', '19440.n1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [375138087093, 148, 87181920000], 'label': '77760.bo.6480.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '6480.cn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.cn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056620
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.cn2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.ed2', '3240.g2', '3240.x2', '3240.cg2', '3240.dc2', '3240.ej2', '3240.ev2', '3240.gb1', '3240.gc1', '3240.gd1', '3240.ge1', '3240.ho1'], 'contains': ['12960.t1', '12960.bh1', '19440.n2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [442641305971, 224515, 448908243571], 'label': '77760.bo.6480.cn2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '6480.cn2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.cn2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056621
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.ee1', '2160.fa1', '3240.ch1', '3240.dd1', '3240.df1', '3240.ga1', '3240.gi1', '3240.hk1', '3240.hp1'], 'contains': ['12960.u1', '12960.bi1', '19440.n1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87182237067, 375138087093, 224612], 'label': '77760.bo.6480.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '6480.co1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.co1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056622
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.co2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.ee2', '3240.ch2', '3240.dd2', '3240.gf1', '3240.gg1', '3240.hp1'], 'contains': ['12960.u1', '12960.bi1', '19440.n2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [442641305971, 143731, 448908243571], 'label': '77760.bo.6480.co2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '6480.co2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.co2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056623
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.ef1', '3240.n1', '3240.bh1', '3240.cj1', '3240.cu1', '3240.cu2', '3240.dg1', '3240.el1', '3240.ev1', '3240.ev2', '3240.ex1', '3240.fx1', '3240.gj1', '3240.gk1', '3240.gn1', '3240.hq1'], 'contains': ['12960.t1', '12960.bm1', '19440.o1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [274468100401, 268244605680, 80880], 'label': '77760.bo.6480.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '6480.cp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.cp1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056624
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.ec1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.ef1', '2160.eg1', '3240.bi1', '3240.bj1', '3240.bw1', '3240.cw1', '3240.cw2', '3240.dh1', '3240.et1', '3240.et2', '3240.ey1', '3240.ez1', '3240.fr1', '3240.gl1', '3240.go1', '3240.gp1', '3240.hr1'], 'contains': ['12960.s1', '12960.bn1', '19440.o1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [268244605587, 274468002505, 80787], 'label': '77760.bo.6480.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '6480.cq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.cq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056625
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.eg1', '3240.l1', '3240.bk1', '3240.cj1', '3240.cx1', '3240.cx2', '3240.di1', '3240.ej1', '3240.ej2', '3240.em1', '3240.fa1', '3240.fy1', '3240.gm1', '3240.gn1', '3240.gq1', '3240.hs1'], 'contains': ['12960.t1', '12960.bo1', '19440.o1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [268244524800, 143975, 274468135825], 'label': '77760.bo.6480.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '6480.cr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.cr1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056626
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.cz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.eh1', '2160.ei1', '3240.bi1', '3240.cc1', '3240.da1', '3240.da2', '3240.dj1', '3240.fb1', '3240.fn1', '3240.fs1', '3240.gl1', '3240.gr1', '3240.hw1'], 'contains': ['12960.s1', '12960.bs1', '19440.p1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [274468060348, 268244605587, 80787], 'label': '77760.bo.6480.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '6480.cs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.cs1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056628
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.bq1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.eh1', '3240.l1', '3240.bh1', '3240.cq1', '3240.dc1', '3240.dc2', '3240.dk1', '3240.en1', '3240.fc1', '3240.fl1', '3240.fl2', '3240.fz1', '3240.gj1', '3240.gm1', '3240.gs1', '3240.hx1'], 'contains': ['12960.t1', '12960.bt1', '19440.p1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [179012, 268244524800, 274468095480], 'label': '77760.bo.6480.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '6480.ct1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.ct1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056629
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.ei1', '3240.cr1', '3240.dd1', '3240.dd2', '3240.dl1', '3240.ga1', '3240.gt1', '3240.hy1'], 'contains': ['12960.u1', '12960.bu1', '19440.p1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [442681119480, 355499199959, 179159], 'label': '77760.bo.6480.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '6480.cu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.cu1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056630
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.cs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.n1', '2160.ej1', '2160.er1', '3240.z1', '3240.bx1', '3240.dm1', '3240.dv1', '3240.ey1', '3240.fd1', '3240.fs1', '3240.ft1'], 'contains': ['12960.s1', '19440.q1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [443120071204, 267845402404, 80787], 'label': '77760.bo.6480.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '6480.cv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.cv1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056631
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.cs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.eq1', '2160.ek1', '2160.es1', '3240.ba1', '3240.by1', '3240.dm1', '3240.dy1', '3240.fe1', '3240.fo1', '3240.fu1', '3240.fw1', '3240.go1', '3240.gr1', '3240.ic1'], 'contains': ['12960.s1', '19440.r1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [482676004, 88695175204, 80787], 'label': '77760.bo.6480.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '6480.cw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.cw1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056632
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.cv1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.er1', '2160.el1', '2160.et1', '3240.bb1', '3240.by1', '3240.db1', '3240.dn1', '3240.ff1', '3240.fp1', '3240.ft1', '3240.gp1', '3240.hw1'], 'contains': ['12960.s1', '19440.s1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [482676004, 88695353644, 80787], 'label': '77760.bo.6480.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '6480.cx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.cx1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056633
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.dv1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.es1', '2160.em1', '2160.en1', '3240.ba1', '3240.bb1', '3240.bz1', '3240.cy1', '3240.do1', '3240.eu1', '3240.fd1', '3240.fg1', '3240.fv1', '3240.gl1', '3240.hr1'], 'contains': ['12960.s1', '19440.t1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [482676004, 80787, 88695348625], 'label': '77760.bo.6480.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '6480.cy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.cy1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056634
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.dv1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.o1', '2160.eo1', '2160.ep1', '3240.z1', '3240.bc1', '3240.ca1', '3240.dh1', '3240.do1', '3240.fb1', '3240.fe1', '3240.ff1', '3240.fr1', '3240.fv1', '3240.gy1'], 'contains': ['12960.s1', '19440.u1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [443120071204, 267845679358, 80787], 'label': '77760.bo.6480.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '6480.cz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.cz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056635
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.cv1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.p1', '2160.eq1', '2160.eu1', '3240.bc1', '3240.bx1', '3240.dj1', '3240.dn1', '3240.ez1', '3240.fg1', '3240.fu1', '3240.hf1'], 'contains': ['12960.s1', '19440.v1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [443120071204, 80787, 267845674052], 'label': '77760.bo.6480.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '6480.da1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.da1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056636
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.q1', '2160.ej1', '3240.h1', '3240.bd1', '3240.ck1', '3240.dp1', '3240.dw1', '3240.el1', '3240.eo1', '3240.fa1', '3240.fh1', '3240.fz1', '3240.gb1'], 'contains': ['12960.t1', '19440.q1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [443120169575, 267845718987, 143975], 'label': '77760.bo.6480.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '6480.db1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.db1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056637
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.et1', '2160.ek1', '3240.i1', '3240.be1', '3240.cl1', '3240.dp1', '3240.dz1', '3240.ep1', '3240.es1', '3240.fi1', '3240.fq1', '3240.gc1', '3240.gh1', '3240.gk1', '3240.gq1', '3240.gs1', '3240.id1'], 'contains': ['12960.t1', '19440.r1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [88695129600, 482630400, 143975], 'label': '77760.bo.6480.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '6480.dc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.dc1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056638
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '108.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.n1', '36.n1', '54.d1'], 'contains': ['216.n1', '216.s1', '216.u1', '324.g1', '540.dy1', '648.n1', '1080.da1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [143975, 174879452158, 462320328386, 143304], 'label': '77760.bo.108.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '108.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.q1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 246056639
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.eu1', '2160.el1', '3240.j1', '3240.bf1', '3240.cl1', '3240.de1', '3240.dq1', '3240.eq1', '3240.fj1', '3240.fm1', '3240.gb1', '3240.gn1', '3240.hx1'], 'contains': ['12960.t1', '19440.s1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [482675904, 88695272904, 80880], 'label': '77760.bo.6480.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '6480.dd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.dd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056640
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.ev1', '2160.em1', '3240.i1', '3240.bf1', '3240.cm1', '3240.cv1', '3240.dr1', '3240.eo1', '3240.ew1', '3240.fk1', '3240.gd1', '3240.gm1', '3240.hq1'], 'contains': ['12960.t1', '19440.t1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [88695170185, 482630400, 143975], 'label': '77760.bo.6480.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '6480.de1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.de1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056641
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['720.ew1', '2160.en1', '3240.j1', '3240.be1', '3240.cm1', '3240.cz1', '3240.ds1', '3240.ek1', '3240.er1', '3240.fh1', '3240.ge1', '3240.gj1', '3240.hs1'], 'contains': ['12960.t1', '19440.t1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [482711044, 88695170185, 45363], 'label': '77760.bo.6480.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '6480.df1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.df1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056642
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.r1', '2160.eo1', '3240.h1', '3240.bg1', '3240.cn1', '3240.dg1', '3240.dr1', '3240.ep1', '3240.fc1', '3240.fj1', '3240.fy1', '3240.ge1', '3240.gu1'], 'contains': ['12960.t1', '19440.u1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [179012, 443120204612, 267845678885], 'label': '77760.bo.6480.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '6480.dg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.dg1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056643
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.s1', '2160.ep1', '3240.k1', '3240.bd1', '3240.cn1', '3240.di1', '3240.ds1', '3240.en1', '3240.eq1', '3240.fi1', '3240.fx1', '3240.gd1', '3240.gz1'], 'contains': ['12960.t1', '19440.u1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [443120025600, 267845397242, 80880], 'label': '77760.bo.6480.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '6480.dh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.dh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056644
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.t1', '2160.eq1', '3240.k1', '3240.bg1', '3240.ck1', '3240.dk1', '3240.dq1', '3240.em1', '3240.er1', '3240.ex1', '3240.fk1', '3240.gc1', '3240.hj1'], 'contains': ['12960.t1', '19440.v1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [179012, 443120204612, 267845674052], 'label': '77760.bo.6480.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '6480.di1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.di1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056645
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.dy1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.u1', '2160.er1', '3240.co1', '3240.dt1', '3240.dx1', '3240.ga1', '3240.gf1'], 'contains': ['12960.u1', '19440.q1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [443120204759, 267845719084, 179159], 'label': '77760.bo.6480.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '6480.dj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.dj1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056646
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.dy1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.ex1', '2160.es1', '3240.cp1', '3240.dt1', '3240.ea1', '3240.gg1', '3240.gi1', '3240.gt1', '3240.ie1'], 'contains': ['12960.u1', '19440.r1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [88695129600, 482630400, 179159], 'label': '77760.bo.6480.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '6480.dk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.dk1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056647
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.ey1', '2160.et1', '3240.cp1', '3240.df1', '3240.du1', '3240.gf1', '3240.hy1'], 'contains': ['12960.u1', '19440.s1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [143731, 482630400, 88695272904], 'label': '77760.bo.6480.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '6480.dl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.dl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056648
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.v1', '2160.eu1', '3240.co1', '3240.dl1', '3240.du1', '3240.gg1', '3240.hk1'], 'contains': ['12960.u1', '19440.v1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [443120250212, 267845674052, 224612], 'label': '77760.bo.6480.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '6480.dm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.dm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056649
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '108.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.s1', '36.t1', '36.u1', '54.a1', '54.b1', '54.g1'], 'contains': ['216.a1', '648.q1', '1080.ic1', '1620.hu1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93924230400, 462320328958], 'label': '77760.bo.108.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.r1', 'subgroup_fusion': None, 'weyl_group': '720.763'}
  • id: 246056650
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.q1', '1620.hu1', '2160.ev1', '2160.ew1', '2160.ex1', '2160.fk1', '3240.f1', '3240.m1', '3240.cb1'], 'contains': ['12960.v1', '12960.x1', '12960.bb1', '19440.m1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [518918400, 442641064349, 997960349], 'label': '77760.bo.6480.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '6480.dn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.dn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056651
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.r1', '1620.hv1', '2160.ey1', '2160.ez1', '2160.fa1', '2160.fl1', '3240.m1', '3240.bu1'], 'contains': ['12960.v1', '12960.bf1', '12960.bj1', '19440.n1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [368871149398, 375138086998, 174436416000], 'label': '77760.bo.6480.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '6480.do1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.do1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056652
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.cw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.fb1', '2160.fc1', '2160.fd1', '2160.fe1', '2160.ff1', '3240.bj1', '3240.cc1', '3240.dv1', '3240.eb1', '3240.gy1', '3240.hd1', '3240.hf1', '3240.hg1', '3240.hr1', '3240.hw1', '3240.ic1'], 'contains': ['12960.s1', '19440.w1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [274467962404, 268244605587, 80787], 'label': '77760.bo.6480.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '6480.dp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.dp1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056653
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.s1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.fb1', '2160.fg1', '2160.fh1', '3240.n1', '3240.bk1', '3240.cq1', '3240.dw1', '3240.ec1', '3240.gu1', '3240.gv1', '3240.gz1', '3240.he1', '3240.hj1', '3240.ho1', '3240.hq1', '3240.hs1', '3240.hx1', '3240.id1'], 'contains': ['12960.t1', '19440.w1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [442680940800, 143975, 355499164775], 'label': '77760.bo.6480.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '6480.dq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.dq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056654
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.ef1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.fc1', '2160.fi1', '2160.fj1', '3240.cr1', '3240.dx1', '3240.ed1', '3240.hk1', '3240.hp1', '3240.hy1', '3240.ie1'], 'contains': ['12960.u1', '19440.w1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [442680940800, 355499199959, 179159], 'label': '77760.bo.6480.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '6480.dr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.dr1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056655
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.bs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.w1', '2160.fd1', '2160.fg1', '2160.fi1', '3240.o1', '3240.cd1', '3240.ee1', '3240.ei1', '3240.gw1', '3240.ha1', '3240.hh1', '3240.hl1', '3240.ht1', '3240.hz1', '3240.if1'], 'contains': ['19440.w1', '25920.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [274467916800, 268244524800, 194518195200], 'label': '77760.bo.6480.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '6480.ds1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.ds1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056656
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.cj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.fd1', '2160.fh1', '2160.fj1', '3240.ce1', '3240.ef1', '3240.hb1', '3240.hi1', '3240.hu1'], 'contains': ['19440.w1', '25920.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [442680940800, 355499020800, 355419232804], 'label': '77760.bo.6480.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.i1', 'old_label': '6480.dt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.dt1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056657
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.fe1', '2160.fg1', '2160.fh1', '3240.p1', '3240.eg1', '3240.gx1', '3240.hc1', '3240.hm1', '3240.hv1', '3240.ia1'], 'contains': ['19440.w1', '25920.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [442680940800, 355499020800, 355419232563], 'label': '77760.bo.6480.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1', 'old_label': '6480.du1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.du1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056658
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.ff1', '2160.fi1', '2160.fj1', '3240.eh1', '3240.hn1', '3240.ib1'], 'contains': ['19440.w1', '25920.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [274467916800, 194518374451, 268244524800], 'label': '77760.bo.6480.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.dx1', 'old_label': '6480.dv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.dv1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246056659
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.fp1', '2160.fq1', '2160.ft1', '2160.fu1', '3240.a1', '3240.x1', '3240.cf1', '3240.cs2', '3240.cs3', '3240.ej1', '3240.ej2'], 'contains': ['12960.w1', '12960.bh1', '12960.bo1', '19440.x1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [148, 375138172555, 87182005805], 'label': '77760.bo.6480.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bd1', 'old_label': '6480.dw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.dw1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056660
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '108.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.v1', '36.w1', '36.x1', '54.b1', '54.f1'], 'contains': ['216.a1', '648.r1', '1080.ie1', '1620.hv1'], 'core': '216.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93924230400, 462320369015], 'label': '77760.bo.108.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '108.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.s1', 'subgroup_fusion': None, 'weyl_group': '720.763'}
  • id: 246056661
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.dw2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.fq2', '3240.a2', '3240.x2', '3240.cf2', '3240.cs1', '3240.cs4', '3240.ej1', '3240.ej2'], 'contains': ['12960.w1', '12960.bh1', '12960.bo1', '19440.x2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [45363, 442641341252, 448908283914], 'label': '77760.bo.6480.dw2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '6480.dw2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.dw2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056662
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.hb1', '2160.fp1', '2160.fr1', '2160.fv1', '2160.fx1', '2160.fz1', '3240.b1', '3240.m1', '3240.bt1'], 'contains': ['12960.x1', '12960.bj1', '12960.bp1', '19440.x1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 6480, 'diagramx': None, 'generators': [368871149398, 375138172555, 174436416000], 'label': '77760.bo.6480.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1620.ba1', 'old_label': '6480.dx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.dx1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056663
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.hc1', '2160.fp1', '2160.fs1', '2160.fw1', '2160.fy1', '3240.c1'], 'contains': ['12960.y1', '12960.bk1', '12960.br1', '19440.x1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 12960, 'diagramx': None, 'generators': [442641109946, 997920598, 519200188], 'label': '77760.bo.6480.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3240.c1', 'old_label': '6480.dy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.dy1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056664
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.bc1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.fq1', '2160.fr1', '2160.fs1', '2160.gd1', '2160.ge1', '3240.u1', '3240.y1', '3240.bp1', '3240.ct1', '3240.ct2', '3240.et1', '3240.et2'], 'contains': ['12960.z1', '12960.be1', '12960.bn1', '19440.x1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [87182277597, 375138172205, 80787], 'label': '77760.bo.6480.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bi1', 'old_label': '6480.dz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.dz1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056665
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.dz2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.p1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.fq2', '2160.ge2', '3240.u2', '3240.y2', '3240.bp2', '3240.ct1', '3240.ct3', '3240.et1', '3240.et2'], 'contains': ['12960.z1', '12960.be1', '12960.bn1', '19440.x2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [448908278999, 442641301050, 80787], 'label': '77760.bo.6480.dz2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '6480.dz2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.dz2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056666
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.he1', '2160.ft1', '2160.fw1', '2160.fx1', '2160.gd1', '2160.gf1', '3240.e1', '3240.m1', '3240.bq1'], 'contains': ['12960.bb1', '12960.bf1', '12960.bp1', '19440.x1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 6480, 'diagramx': None, 'generators': [368871153961, 375138086998, 174436416000], 'label': '77760.bo.6480.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1620.ba1', 'old_label': '6480.ea1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.ea1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056667
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.hf1', '2160.fu1', '2160.fv1', '2160.fy1', '2160.gd1', '2160.gg1', '3240.br1'], 'contains': ['12960.bc1', '12960.bg1', '12960.bq1', '19440.x1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 12960, 'diagramx': None, 'generators': [518964004, 997925759, 442641024450], 'label': '77760.bo.6480.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3240.br1', 'old_label': '6480.eb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.eb1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056668
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.fz1', '2160.ge1', '2160.gf1', '2160.gg1', '3240.g1', '3240.t1', '3240.cf1', '3240.cs1', '3240.cs3', '3240.ev1', '3240.ev2'], 'contains': ['12960.ba1', '12960.bh1', '12960.bm1', '19440.x1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [87182196721, 143975, 375138172555], 'label': '77760.bo.6480.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bd1', 'old_label': '6480.ec1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.ec1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056669
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.ec2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.ge2', '3240.g2', '3240.t2', '3240.cf2', '3240.cs2', '3240.cs4', '3240.ev1', '3240.ev2'], 'contains': ['12960.ba1', '12960.bh1', '12960.bm1', '19440.x2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [179012, 448908284158, 442641341252], 'label': '77760.bo.6480.ec2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '6480.ec2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.ec2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056670
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.ga1', '2160.gh1', '2160.gi1', '3240.a1', '3240.t1', '3240.ci1', '3240.cs3', '3240.cs4', '3240.fl1', '3240.fl2'], 'contains': ['12960.w1', '12960.ba1', '12960.bt1', '19440.y1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [45363, 375138172205, 87182282615], 'label': '77760.bo.6480.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bd1', 'old_label': '6480.ed1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.ed1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056671
    {'ambient': '77760.bo', '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': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.a1', '60.m1'], 'contains': ['240.a1', '240.c1', '240.d1', '240.bk1', '240.bm1', '240.cg1', '240.cm1', '360.a1', '360.f1', '360.h1', '360.i1', '360.j1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [180587456184, 40349, 174400208787, 93449036612, 83606375, 143975, 80787], 'label': '77760.bo.120.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '120.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.a1', 'subgroup_fusion': None, 'weyl_group': '1296.3538'}
  • id: 246056672
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.ed2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.gi2', '3240.a2', '3240.t2', '3240.ci2', '3240.cs1', '3240.cs2', '3240.fl1', '3240.fl2'], 'contains': ['12960.w1', '12960.ba1', '12960.bt1', '19440.y2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [448908283441, 442641346558, 224515], 'label': '77760.bo.6480.ed2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '6480.ed2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.ed2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056673
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.hi1', '2160.ga1', '2160.gb1', '2160.gc1', '2160.gh1', '2160.gj1', '3240.b1', '3240.e1', '3240.cb1'], 'contains': ['12960.x1', '12960.bb1', '12960.bv1', '19440.y1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 6480, 'diagramx': None, 'generators': [368871234955, 375138172205, 174436416000], 'label': '77760.bo.6480.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1620.ba1', 'old_label': '6480.ee1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.ee1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056674
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1620.hj1', '2160.gb1', '2160.gh1', '2160.gk1', '3240.c1'], 'contains': ['12960.y1', '12960.bd1', '12960.bw1', '19440.y1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 12960, 'diagramx': None, 'generators': [997925759, 519235320, 442641029309], 'label': '77760.bo.6480.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3240.c1', 'old_label': '6480.ef1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.ef1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056675
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.gi1', '2160.gj1', '2160.gk1', '3240.u1', '3240.bv1', '3240.ct2', '3240.ct3', '3240.fn1'], 'contains': ['12960.z1', '12960.bs1', '19440.y1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [87182202116, 375138172205, 80787], 'label': '77760.bo.6480.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bi1', 'old_label': '6480.eg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.eg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056676
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.eg2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.gi2', '3240.u2', '3240.bv2', '3240.ct1', '3240.fn1'], 'contains': ['12960.z1', '12960.bs1', '19440.y2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [448908001949, 442641301050, 80787], 'label': '77760.bo.6480.eg2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '6480.eg2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.eg2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056677
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.gl1', '3240.l1', '3240.bh1', '3240.cj1', '3240.cs1', '3240.cs2', '3240.cs3', '3240.cs4'], 'contains': ['12960.bm1', '12960.bo1', '12960.bt1', '19440.z1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [268244703480, 179012, 274468002505], 'label': '77760.bo.6480.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bd1', 'old_label': '6480.eh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.eh1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056678
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '6480.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.gl1', '3240.bi1', '3240.bw1', '3240.ct1', '3240.ct2', '3240.ct3'], 'contains': ['12960.bn1', '12960.bs1', '19440.z1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [268244748747, 274468002505, 80787], 'label': '77760.bo.6480.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bi1', 'old_label': '6480.ei1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.ei1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056679
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '7776.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.a1', '2592.b1', '2592.c1', '3888.a1', '3888.b1', '3888.c1'], 'contains': ['15552.a1', '38880.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [138242, 18764663042], 'label': '77760.bo.7776.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d1', 'old_label': '7776.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 246056680
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '7776.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.d1', '2592.e1', '2592.f1', '3888.c1', '3888.d1', '3888.e1'], 'contains': ['15552.a1', '38880.b1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [178680, 18764703480], 'label': '77760.bo.7776.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.e1', 'old_label': '7776.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 246056681
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '7776.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.w1', '2592.g1', '2592.h1', '2592.i1', '3888.a1', '3888.d1', '3888.f1', '3888.g1', '3888.h1'], 'contains': ['15552.a1', '38880.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1037836800, 18764524800], 'label': '77760.bo.7776.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '7776.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.c1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 246056682
    {'ambient': '77760.bo', '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': '25920.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.b1', '60.a1', '60.b1', '60.m1'], 'contains': ['240.a1', '240.b1', '240.bi1', '240.br1', '240.bw1', '360.b1', '360.k1', '360.l1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [180587277504, 86155, 456053074316, 93448857748, 174400173363, 80880, 80787], 'label': '77760.bo.120.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '120.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.b1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 246056683
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '7776.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.j1', '2592.k1', '2592.l1', '3888.a1', '3888.b1', '3888.e1'], 'contains': ['15552.a1', '38880.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [18764524800, 1038020645], 'label': '77760.bo.7776.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d1', 'old_label': '7776.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.d1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 246056684
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '7776.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.m1', '2592.n1', '2592.o1', '3888.b1', '3888.d1'], 'contains': ['15552.a1', '38880.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1037980104, 18764524800], 'label': '77760.bo.7776.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.e1', 'old_label': '7776.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.e1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 246056685
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '8640.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.b1', 'complements': ['9.a1'], 'conjugacy_class_count': 2, 'contained_in': ['1728.a1', '2880.a1', '2880.b1', '2880.c1', '4320.a1', '4320.e1', '4320.l1', '4320.r1', '4320.bh1', '4320.bo1', '4320.bz1', '4320.cf1', '4320.cw1', '4320.cz1', '4320.di1'], 'contains': ['25920.a1', '25920.b1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [143975, 80787], 'label': '77760.bo.8640.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8640.a1', 'normal_contained_in': ['24.a1', '2880.a1', '4320.a1'], 'normal_contains': ['25920.a1'], 'normalizer': '1.a1', 'old_label': '8640.a1', 'projective_image': '77760.bo', 'quotient_action_image': '12.4', 'quotient_action_kernel': '720.763', 'quotient_action_kernel_order': 720, 'quotient_fusion': None, 'short_label': '8640.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056686
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '8640.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.b1', '2880.a1', '2880.d1', '2880.e1', '4320.m1', '4320.s1', '4320.bi1', '4320.cg1', '4320.dj1'], 'contains': ['25920.a1', '25920.c1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [80787, 179159], 'label': '77760.bo.8640.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2880.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '8640.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8640.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056687
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '8640.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '80.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.fd1', '2880.b1', '2880.d1', '2880.f1', '2880.g1', '2880.h1', '4320.f1', '4320.i1', '4320.t1', '4320.ba1', '4320.bj1', '4320.bp1', '4320.ca1', '4320.ce1', '4320.ch1', '4320.da1', '4320.dk1'], 'contains': ['25920.a1', '25920.d1', '25920.e1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [194518195200, 80787], 'label': '77760.bo.8640.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '8640.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8640.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056688
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '8640.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '480.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.fe1', '2880.b1', '2880.c1', '2880.e1', '2880.f1', '2880.i1', '2880.i2', '4320.g1', '4320.u1', '4320.bq1', '4320.cb1', '4320.ci1', '4320.db1', '4320.dl1'], 'contains': ['25920.a1', '25920.f1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 160, 'diagramx': None, 'generators': [355419232563, 80787], 'label': '77760.bo.8640.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.a1', 'old_label': '8640.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8640.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246056689
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '8640.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '480.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.ff1', '2880.c1', '2880.d1', '2880.e1', '2880.g1', '2880.i1', '2880.i2', '4320.v1', '4320.cj1', '4320.dm1'], 'contains': ['25920.a1', '25920.g1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 160, 'diagramx': None, 'generators': [355419504028, 80787], 'label': '77760.bo.8640.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '80.k1', 'old_label': '8640.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8640.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056690
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '8640.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '240.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.fg1', '2880.b1', '2880.j1', '2880.k1', '4320.b1', '4320.h1', '4320.n1', '4320.w1', '4320.bb1', '4320.bk1', '4320.bn1', '4320.br1', '4320.bs1', '4320.cc1', '4320.ck1', '4320.cu1', '4320.cx1', '4320.dc1', '4320.dn1'], 'contains': ['25920.b1', '25920.d1', '25920.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [143975, 355419549387], 'label': '77760.bo.8640.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '8640.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8640.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056691
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '8640.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '480.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2160.fh1', '2880.b1', '2880.j1', '4320.o1', '4320.x1', '4320.bt1', '4320.cd1', '4320.cl1', '4320.cy1', '4320.dd1'], 'contains': ['25920.b1', '25920.e1', '25920.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [143975, 355419504120], 'label': '77760.bo.8640.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.v1', 'old_label': '8640.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8640.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056692
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '8640.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '480.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.fi1', '2880.d1', '2880.l1', '2880.m1', '4320.p1', '4320.y1', '4320.bc1', '4320.bl1', '4320.cm1', '4320.cv1', '4320.do1'], 'contains': ['25920.c1', '25920.d1', '25920.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [355419549484, 179159], 'label': '77760.bo.8640.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.x1', 'old_label': '8640.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8640.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056693
    {'ambient': '77760.bo', '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': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.c1', '60.a1', '60.c1', '60.m1'], 'contains': ['240.b1', '240.c1', '240.bx1', '240.by1', '240.cj1', '360.c1', '360.n1', '360.q1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [143975, 80787, 174400208787, 93449036612, 180587232000, 456053154955, 85805], 'label': '77760.bo.120.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '120.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.c1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246056694
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '8640.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '480.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.fj1', '2880.d1', '2880.l1', '4320.q1', '4320.z1', '4320.cn1'], 'contains': ['25920.c1', '25920.e1', '25920.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [355419504267, 179159], 'label': '77760.bo.8640.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.u1', 'old_label': '8640.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8640.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056695
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '8640.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '160.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2880.h1', '2880.j1', '2880.l1', '4320.j1', '4320.bd1', '4320.bu1', '4320.co1', '4320.de1'], 'contains': ['25920.d1', '25920.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 80, 'diagramx': None, 'generators': [280259481600, 193999357587], 'label': '77760.bo.8640.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.h1', 'old_label': '8640.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8640.j1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056696
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '8640.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '480.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2880.f1', '2880.j1', '2880.k1', '4320.c1', '4320.be1', '4320.bv1', '4320.bw1', '4320.cp1', '4320.df1', '4320.dp1'], 'contains': ['25920.d1', '25920.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [280259625575, 193999420775], 'label': '77760.bo.8640.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1', 'old_label': '8640.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8640.k1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056697
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '8640.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '960.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2880.g1', '2880.l1', '2880.m1', '4320.bf1', '4320.cq1', '4320.dq1'], 'contains': ['25920.d1', '25920.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [280259705975, 193999501175], 'label': '77760.bo.8640.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.bp1', 'old_label': '8640.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8640.l1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056698
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '8640.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '80.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2880.h1', '2880.k1', '2880.m1', '4320.d1', '4320.k1', '4320.bg1', '4320.bm1', '4320.bx1', '4320.cr1', '4320.dg1', '4320.dr1'], 'contains': ['25920.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 10, 'diagramx': None, 'generators': [280259481600, 193999276800], 'label': '77760.bo.8640.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '8640.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8640.m1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 246056699
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '8640.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '960.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2880.f1', '2880.j1', '4320.by1', '4320.cs1', '4320.dh1'], 'contains': ['25920.e1', '25920.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 960, 'diagramx': None, 'generators': [280259527104, 193999357587], 'label': '77760.bo.8640.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.cg1', 'old_label': '8640.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8640.n1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056700
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '8640.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '960.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2880.g1', '2880.l1', '4320.ct1'], 'contains': ['25920.e1', '25920.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 960, 'diagramx': None, 'generators': [280259562387, 193999420531], 'label': '77760.bo.8640.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '480.ba1', 'old_label': '8640.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8640.o1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056701
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.a1', '3240.b1', '3240.c1', '3240.e1', '3240.t1', '3240.u1', '4860.e1', '4860.e2', '4860.r1'], 'contains': ['19440.a1', '19440.c1', '19440.d1', '19440.j1', '19440.k1', '19440.x1', '19440.y1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 9720, 'diagramx': None, 'generators': [86155, 442641024000, 443120026293], 'label': '77760.bo.9720.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2430.j1', 'old_label': '9720.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056702
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.a2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1215.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.a2', '3240.t2', '3240.u2', '4860.e1', '4860.e2', '4860.r2'], 'contains': ['19440.a1', '19440.c1', '19440.d1', '19440.j2', '19440.k2', '19440.x2', '19440.y2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [448908284158, 442641341252, 322558], 'label': '77760.bo.9720.a2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '9720.a2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056703
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bd1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.d1', '3240.f1', '3240.v1', '3240.w1', '4860.c1', '4860.d1', '4860.e2', '4860.f1', '4860.g1', '4860.h1', '4860.r1'], 'contains': ['19440.a1', '19440.b1', '19440.j1', '19440.l1', '19440.m1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [86155, 87182006155, 375138172555], 'label': '77760.bo.9720.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '9720.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056704
    {'ambient': '77760.bo', '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': '25920.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '40.d1', '60.b1', '60.c1', '60.n1'], 'contains': ['240.b1', '240.ca1', '240.cc1', '360.d1', '360.r1', '1080.y1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [88695170185, 280259567405, 143975, 193999455812, 85805, 80787, 482670985], 'label': '77760.bo.120.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '120.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.d1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 246056705
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.b2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '405.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.d2', '3240.v2', '3240.w2', '4860.a1', '4860.b1', '4860.e1', '4860.h1', '4860.r2'], 'contains': ['19440.a1', '19440.b1', '19440.j2', '19440.l2', '19440.m2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [40349, 442641024000, 448908001949], 'label': '77760.bo.9720.b2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '9720.b2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056706
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.g1', '3240.m1', '3240.x1', '3240.y1', '4860.d1', '4860.e1', '4860.k1', '4860.l1', '4860.n1', '4860.o1', '4860.r1'], 'contains': ['19440.b1', '19440.c1', '19440.m1', '19440.n1', '19440.x1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [85805, 375138172555, 87182005805], 'label': '77760.bo.9720.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '9720.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056707
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.c2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1215.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.g2', '3240.x2', '3240.y2', '4860.e2', '4860.i1', '4860.j1', '4860.o1', '4860.r2'], 'contains': ['19440.b1', '19440.c1', '19440.m2', '19440.n2', '19440.x2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [5309, 448908284158, 442641341252], 'label': '77760.bo.9720.c2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '9720.c2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.c2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056708
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1944.a1', '3240.h1', '3240.z1', '3240.bd1', '4860.a1', '4860.f1', '4860.i1', '4860.k1', '4860.s1'], 'contains': ['19440.b1', '19440.q1', '19440.u1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [443120025600, 267845397242, 40442], 'label': '77760.bo.9720.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '9720.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056709
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.j1', '3240.i1', '3240.ba1', '3240.be1', '4860.a1', '4860.g1', '4860.j1', '4860.l1', '4860.m1', '4860.q1', '4860.t1'], 'contains': ['19440.b1', '19440.r1', '19440.t1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [88695170185, 40585, 482670985], 'label': '77760.bo.9720.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '9720.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056710
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.k1', '3240.j1', '3240.bb1', '3240.bf1', '4860.b1', '4860.d1', '4860.i1', '4860.p1', '4860.t1'], 'contains': ['19440.b1', '19440.s1', '19440.t1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [482849425, 219025, 88695170185], 'label': '77760.bo.9720.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '9720.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056711
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1944.b1', '3240.k1', '3240.bc1', '3240.bg1', '4860.b1', '4860.c1', '4860.j1', '4860.n1', '4860.s1'], 'contains': ['19440.b1', '19440.u1', '19440.v1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [443120025600, 138242, 267845397242], 'label': '77760.bo.9720.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '9720.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056712
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.l1', '3240.bh1', '3240.bi1', '4860.c1', '4860.e1', '4860.e2', '4860.k1', '4860.m1', '4860.p1', '4860.u1'], 'contains': ['19440.b1', '19440.d1', '19440.o1', '19440.p1', '19440.z1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [183845, 268244524800, 274468095480], 'label': '77760.bo.9720.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '9720.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056713
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bd1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.n1', '3240.o1', '3240.p1', '3240.bj1', '3240.bk1', '4860.f1', '4860.h1', '4860.n1', '4860.o1', '4860.p1', '4860.q1', '4860.u1'], 'contains': ['19440.b1', '19440.o1', '19440.w1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [183845, 274467916800, 268244524800], 'label': '77760.bo.9720.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '9720.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.i1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056714
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '405.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.q1', '3240.r1', '3240.bl1', '3240.bn1', '4860.r1', '4860.r2'], 'contains': ['19440.a1', '19440.c1', '19440.e1', '19440.f1', '19440.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [442641024000, 85805, 143304], 'label': '77760.bo.9720.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '9720.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056715
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.e1', '60.a1', '60.n1'], 'contains': ['240.b1', '240.cb1', '240.cd1', '360.e1', '360.s1', '1080.z1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [183845, 88695170185, 280259700485, 482768881, 80880, 80787, 193999357587], 'label': '77760.bo.120.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '120.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.e1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246056716
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1215.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.c1', '3240.s1', '3240.bm1', '3240.bo1', '4860.r1', '4860.r2', '4860.s1', '4860.t1', '4860.u1'], 'contains': ['19440.b1', '19440.d1', '19440.e1', '19440.g1', '19440.i1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1215, 'diagramx': None, 'generators': [274467916800, 85805, 143304], 'label': '77760.bo.9720.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '9720.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056717
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.bp1', '3240.bq1', '3240.br1', '3240.bt1', '3240.cf1', '4860.r1', '4860.v1', '4860.v2'], 'contains': ['19440.f1', '19440.h1', '19440.i1', '19440.j1', '19440.x1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [443120066185, 442641024000, 143304], 'label': '77760.bo.9720.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2430.j1', 'old_label': '9720.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056718
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.l2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1215.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.bp2', '3240.cf2', '4860.r2', '4860.v1', '4860.v2'], 'contains': ['19440.f1', '19440.h1', '19440.i1', '19440.j2', '19440.x2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [442641109946, 281971, 448908243571], 'label': '77760.bo.9720.l2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '9720.l2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.l2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056719
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.bs1', '3240.bu1', '3240.cg1', '3240.ch1', '4860.r1', '4860.v2', '4860.w1', '4860.x1', '4860.ba1', '4860.bb1', '4860.bc1'], 'contains': ['19440.f1', '19440.g1', '19440.k1', '19440.l1', '19440.n1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [443120025600, 442641024000, 143304], 'label': '77760.bo.9720.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '9720.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.m1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056720
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.m2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '405.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3240.bs2', '3240.cg2', '3240.ch2', '4860.r2', '4860.v1', '4860.y1', '4860.z1', '4860.bc1'], 'contains': ['19440.f1', '19440.g1', '19440.k2', '19440.l2', '19440.n2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [281971, 442641024000, 448908243571], 'label': '77760.bo.9720.m2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '9720.m2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.m2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056721
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.bv1', '3240.cb1', '3240.ci1', '4860.r1', '4860.v1', '4860.w1', '4860.bd1', '4860.bg1', '4860.bi1', '4860.bj1'], 'contains': ['19440.g1', '19440.h1', '19440.m1', '19440.y1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [443120025600, 178680, 442641109705], 'label': '77760.bo.9720.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '9720.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056722
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.n2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1215.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3240.bv2', '3240.ci2', '4860.r2', '4860.v2', '4860.be1', '4860.bf1', '4860.bj1'], 'contains': ['19440.g1', '19440.h1', '19440.m2', '19440.y2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1215, 'diagramx': None, 'generators': [448908284158, 317252, 442641029309], 'label': '77760.bo.9720.n2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '9720.n2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.n2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056723
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.bw1', '3240.cj1', '4860.u1', '4860.v1', '4860.v2', '4860.x1', '4860.bd1', '4860.bh1', '4860.bk1'], 'contains': ['19440.g1', '19440.i1', '19440.o1', '19440.z1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [178680, 268244524800, 274468002505], 'label': '77760.bo.9720.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '9720.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.o1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056724
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.d1', '3240.bx1', '3240.ck1', '3240.co1', '4860.s1', '4860.y1', '4860.ba1', '4860.bd1', '4860.be1'], 'contains': ['19440.g1', '19440.q1', '19440.v1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [443120025600, 317252, 267845674052], 'label': '77760.bo.9720.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '9720.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.p1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056725
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.ci1', '3240.by1', '3240.cl1', '3240.cp1', '4860.t1', '4860.y1', '4860.bb1', '4860.bf1', '4860.bg1', '4860.bh1', '4860.bl1'], 'contains': ['19440.g1', '19440.r1', '19440.s1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [88695272904, 482773704, 143304], 'label': '77760.bo.9720.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '9720.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.q1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056745
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.do1', '3240.dr1', '3240.ds1', '4860.a1', '4860.b1', '4860.z1', '4860.bm1', '4860.bw1'], 'contains': ['19440.l2', '19440.t1', '19440.u1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [7185029309, 19678982400, 462320006400], 'label': '77760.bo.9720.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '9720.bd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.bd1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056726
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.a1', 'complements': ['6480.w1', '6480.u1', '6480.bq1', '6480.k1', '6480.eh1', '6480.m1', '6480.ec2', '6480.ec1', '6480.h1', '6480.j1', '6480.ed2', '6480.ed1', '6480.bp1', '6480.ef1', '6480.s1', '6480.dw1', '6480.dw2', '6480.dy1'], 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '6.a1', '6.b1', '6.g1'], 'contains': ['24.a1', '36.a1', '36.q1', '72.k1', '120.bn1', '180.ee1'], 'core': '12.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [462320323320, 143975, 93924409412, 80787], 'label': '77760.bo.12.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': ['4.c1', '6.a1'], 'normal_contains': ['24.a1', '36.a1'], 'normalizer': '1.a1', 'old_label': '12.b1', 'projective_image': '77760.bo', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.b1', 'subgroup_fusion': None, 'weyl_group': '8640.t'}
  • id: 246056727
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['30.a1', '40.a1', '60.o1'], 'contains': ['240.e1', '240.n1', '240.q1', '240.bf1', '240.bg1', '240.ch1', '240.cn1', '360.f1', '360.z1', '360.ba1', '360.bb1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [183845, 442641386424, 143975, 997965813, 519235320, 80880, 80787], 'label': '77760.bo.120.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '120.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.f1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246056728
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.cj1', '3240.bz1', '3240.cm1', '4860.t1', '4860.w1', '4860.z1', '4860.be1', '4860.bk1'], 'contains': ['19440.g1', '19440.t1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1215, 'diagramx': None, 'generators': [482854584, 224184, 88695348625], 'label': '77760.bo.9720.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '9720.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.r1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056729
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.e1', '3240.ca1', '3240.cn1', '4860.s1', '4860.x1', '4860.z1', '4860.bf1', '4860.bi1'], 'contains': ['19440.g1', '19440.u1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1215, 'diagramx': None, 'generators': [362615, 443120025600, 267845679358], 'label': '77760.bo.9720.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '9720.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.s1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056730
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.cc1', '3240.cd1', '3240.ce1', '3240.cq1', '3240.cr1', '4860.u1', '4860.ba1', '4860.bc1', '4860.bi1', '4860.bj1', '4860.bk1', '4860.bl1'], 'contains': ['19440.g1', '19440.p1', '19440.w1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [274467916800, 268244524800, 143304], 'label': '77760.bo.9720.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '9720.t1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.t1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056731
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.cs1', '3240.cs2', '3240.ct1', '4860.e1', '4860.e2', '4860.v2'], 'contains': ['19440.j1', '19440.j2', '19440.k1', '19440.x1', '19440.x2', '19440.y2', '19440.z1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 9720, 'diagramx': None, 'generators': [19679264371, 448908243571, 462320046749], 'label': '77760.bo.9720.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2430.j1', 'old_label': '9720.u1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.u1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056732
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.u2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.cs3', '3240.ct2', '4860.e1', '4860.v1'], 'contains': ['19440.j2', '19440.k2', '19440.x1', '19440.y1', '19440.z1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [19679161080, 461841090505, 462320006400], 'label': '77760.bo.9720.u2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2430.j1', 'old_label': '9720.u2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.u2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056733
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.u3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.cs4', '3240.ct3', '4860.e2', '4860.v1'], 'contains': ['19440.j1', '19440.k2', '19440.x2', '19440.y1', '19440.z1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [19679304958, 448908284158, 462320046985], 'label': '77760.bo.9720.u3', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2430.j1', 'old_label': '9720.u3', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.u3', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056734
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bd1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.cu1', '3240.cw1', '3240.cx1', '4860.e1', '4860.h1', '4860.v1', '4860.bm1', '4860.bp1', '4860.bq1', '4860.bw1'], 'contains': ['19440.j1', '19440.j2', '19440.l2', '19440.m1', '19440.o1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [461841223825, 19678982400, 462320006400], 'label': '77760.bo.9720.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '9720.v1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.v1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056735
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.v2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bd1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.cu2', '3240.cw2', '3240.cx2', '4860.e2', '4860.h1', '4860.v2', '4860.bn1', '4860.bo1', '4860.bs1', '4860.bu1'], 'contains': ['19440.j1', '19440.j2', '19440.l1', '19440.m2', '19440.o1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [19678982400, 448907961600, 462320328958], 'label': '77760.bo.9720.v2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '9720.v2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.v2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056736
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.ck2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.eq1', '3240.cv1', '3240.cy1', '3240.cz1', '4860.d1', '4860.g1', '4860.w1', '4860.bm2', '4860.bo1', '4860.bs1', '4860.bw1'], 'contains': ['19440.l1', '19440.m1', '19440.t1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [87261753600, 456053073961, 83462400], 'label': '77760.bo.9720.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '9720.w1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.w1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056737
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.da1', '3240.dc1', '3240.dd1', '4860.e1', '4860.bc1', '4860.bm1', '4860.br1', '4860.bx1'], 'contains': ['19440.k1', '19440.k2', '19440.l2', '19440.n1', '19440.p1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [19678982400, 448908243571, 462320006400], 'label': '77760.bo.9720.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '9720.x1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.x1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056738
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.a1'], 'contains': ['240.f1', '240.k1', '240.o1', '240.bh1', '240.bl1', '240.ci1', '240.cl1', '360.i1', '360.ba1', '360.bd1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [180587456184, 183845, 456053207518, 93449036612, 143975, 174400173363, 80787], 'label': '77760.bo.120.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.g1', 'old_label': '120.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.g1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246056739
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.x2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.da2', '3240.dc2', '3240.dd2', '4860.e2', '4860.bc1', '4860.bm2', '4860.bt1', '4860.bv1'], 'contains': ['19440.k1', '19440.k2', '19440.l1', '19440.n2', '19440.p1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [19679264371, 448908243571, 462320006400], 'label': '77760.bo.9720.x2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '9720.x2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.x2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056740
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.co2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.er1', '3240.db1', '3240.de1', '3240.df1', '4860.d1', '4860.bb1', '4860.bn1', '4860.bt1', '4860.bx1'], 'contains': ['19440.l1', '19440.n1', '19440.s1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [87261753600, 456053069398, 83462400], 'label': '77760.bo.9720.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '9720.y1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.y1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056741
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.ck2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.dg1', '3240.dh1', '3240.di1', '4860.c1', '4860.f1', '4860.x1', '4860.bm2', '4860.bn1', '4860.bu1', '4860.bw1'], 'contains': ['19440.l1', '19440.o1', '19440.u1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [443120025600, 442641024000, 180667203842], 'label': '77760.bo.9720.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '9720.z1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.z1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056742
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.co2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.dj1', '3240.dk1', '3240.dl1', '4860.c1', '4860.ba1', '4860.bo1', '4860.bv1', '4860.bx1'], 'contains': ['19440.l1', '19440.p1', '19440.v1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [482854584, 375138086400, 87181920000], 'label': '77760.bo.9720.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '9720.ba1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.ba1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056743
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '90.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3240.dm1', '3240.dp1', '3240.dt1', '4860.a1', '4860.y1', '4860.bp1', '4860.br1', '4860.by1'], 'contains': ['19440.l2', '19440.q1', '19440.r1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [19678982400, 7185024000, 462320006400], 'label': '77760.bo.9720.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '9720.bb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.bb1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056744
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3240.dn1', '3240.dq1', '3240.du1', '4860.b1', '4860.y1', '4860.bq1', '4860.bx1'], 'contains': ['19440.l2', '19440.s1', '19440.v1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [19678982400, 462320006400, 7185202680], 'label': '77760.bo.9720.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '9720.bc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.bc1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056746
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.bv2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.dv1', '3240.dw1', '3240.dx1', '3240.ei1', '4860.f1', '4860.ba1', '4860.bs1', '4860.bt1', '4860.by1'], 'contains': ['19440.l1', '19440.q1', '19440.w1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [443120025600, 442641024000, 180667065600], 'label': '77760.bo.9720.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '9720.be1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.be1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056747
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.bv2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.es1', '3240.dy1', '3240.dz1', '3240.ea1', '4860.g1', '4860.bb1', '4860.bu1', '4860.bv1', '4860.by1'], 'contains': ['19440.l1', '19440.r1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [456053068800, 87261753600, 83462400], 'label': '77760.bo.9720.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '9720.bf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.bf1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056748
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '90.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.eb1', '3240.ec1', '3240.ed1', '3240.ee1', '3240.ef1', '3240.eg1', '3240.eh1', '4860.h1', '4860.bc1', '4860.bw1', '4860.bx1', '4860.by1'], 'contains': ['19440.l1', '19440.l2', '19440.w1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [19678982400, 448907961600, 462320006400], 'label': '77760.bo.9720.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '9720.bg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.bg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056749
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.a1', '60.m1'], 'contains': ['240.g1', '240.l1', '240.p1', '240.bi1', '240.bm1', '240.cj1', '240.cm1', '360.g1', '360.j1', '360.z1', '360.bd1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [180587456184, 93448857748, 174400173363, 456053073961, 85805, 80880, 80787], 'label': '77760.bo.120.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '120.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.h1', 'subgroup_fusion': None, 'weyl_group': '1296.3538'}
  • id: 246056750
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.ej1', '3240.et1', '3240.ev1', '4860.e1', '4860.o1', '4860.v2', '4860.bn1', '4860.bz1', '4860.ca1', '4860.cf1'], 'contains': ['19440.m2', '19440.n1', '19440.o1', '19440.x1', '19440.x2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [19678982400, 448908243571, 462320046749], 'label': '77760.bo.9720.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '9720.bh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.bh1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056751
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.bh2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.ej2', '3240.et2', '3240.ev2', '4860.e2', '4860.o1', '4860.v1', '4860.bm2', '4860.cb1', '4860.cc1', '4860.ce1'], 'contains': ['19440.m1', '19440.n2', '19440.o1', '19440.x1', '19440.x2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [19678987709, 448908284158, 462320328958], 'label': '77760.bo.9720.bh2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '9720.bh2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.bh2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056752
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1080.ib1', '3240.ek1', '3240.eu1', '3240.ew1', '4860.d1', '4860.l1', '4860.w1', '4860.bm1', '4860.ca1', '4860.ce1', '4860.cf1'], 'contains': ['19440.m1', '19440.n1', '19440.t1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [87261753600, 456053069398, 83467561], 'label': '77760.bo.9720.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '9720.bi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.bi1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056753
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.ck2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.el1', '3240.ey1', '3240.fa1', '4860.f1', '4860.k1', '4860.bd1', '4860.bp1', '4860.bs1', '4860.ca1', '4860.cb1'], 'contains': ['19440.m1', '19440.o1', '19440.q1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [482716205, 375138172205, 87181920000], 'label': '77760.bo.9720.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '9720.bj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.bj1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056754
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.em1', '3240.ex1', '3240.ez1', '4860.c1', '4860.n1', '4860.bd1', '4860.bo1', '4860.bq1', '4860.cc1', '4860.cf1'], 'contains': ['19440.m1', '19440.o1', '19440.v1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [375138172555, 482716346, 87181920000], 'label': '77760.bo.9720.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '9720.bk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.bk1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056755
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.en1', '3240.fb1', '3240.fc1', '4860.c1', '4860.k1', '4860.bi1', '4860.bm1', '4860.bm2', '4860.cd1', '4860.cg1'], 'contains': ['19440.m1', '19440.p1', '19440.u1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [443120025600, 180667244280, 442641109705], 'label': '77760.bo.9720.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '9720.bl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.bl1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056756
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.eo1', '3240.fd1', '3240.fh1', '4860.a1', '4860.i1', '4860.be1', '4860.bs1', '4860.ca1'], 'contains': ['19440.m2', '19440.q1', '19440.t1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [19678982400, 7185024000, 462320046985], 'label': '77760.bo.9720.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '9720.bm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.bm1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056757
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.ep1', '3240.fe1', '3240.fi1', '4860.a1', '4860.j1', '4860.bf1', '4860.bu1', '4860.bz1', '4860.cd1', '4860.ch1'], 'contains': ['19440.m2', '19440.r1', '19440.u1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [7185207845, 462320190245, 19678982400], 'label': '77760.bo.9720.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '9720.bn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.bn1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056758
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.eq1', '3240.ff1', '3240.fj1', '4860.b1', '4860.i1', '4860.bf1', '4860.bn1', '4860.cg1'], 'contains': ['19440.m2', '19440.s1', '19440.u1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [462320092205, 7185207845, 19678982400], 'label': '77760.bo.9720.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '9720.bo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.bo1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056759
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.er1', '3240.fg1', '3240.fk1', '4860.b1', '4860.j1', '4860.be1', '4860.bo1', '4860.cf1'], 'contains': ['19440.m2', '19440.t1', '19440.v1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [19678982400, 462320046842, 7185202680], 'label': '77760.bo.9720.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '9720.bp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.bp1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056760
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['30.b1', '40.a1', '60.o1'], 'contains': ['240.h1', '240.m1', '240.q1', '240.bj1', '240.bn1', '240.ck1', '240.cn1', '360.h1', '360.bb1', '360.bd1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [183845, 174436599746, 143975, 375138270474, 80880, 80787, 368871154316], 'label': '77760.bo.120.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '120.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.i1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246056761
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.fl1', '3240.fl2', '3240.fn1', '4860.e1', '4860.e2', '4860.bj1', '4860.bo1', '4860.ca1', '4860.cd1', '4860.cg1'], 'contains': ['19440.m1', '19440.m2', '19440.p1', '19440.y1', '19440.y2'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [19678982400, 448908284158, 462320046985], 'label': '77760.bo.9720.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '9720.bq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.bq1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056762
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.ck2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.ic1', '3240.es1', '3240.fo1', '3240.fq1', '4860.g1', '4860.l1', '4860.bg1', '4860.bp1', '4860.cc1', '4860.cd1', '4860.ch1'], 'contains': ['19440.m1', '19440.r1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [87261753600, 83548555, 456053154955], 'label': '77760.bo.9720.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '9720.br1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.br1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056763
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1080.id1', '3240.fm1', '3240.fp1', '4860.d1', '4860.bg1', '4860.bq1', '4860.cb1', '4860.cg1'], 'contains': ['19440.m1', '19440.s1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [87261753600, 83548346, 456053154955], 'label': '77760.bo.9720.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '9720.bs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.bs1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056764
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.fr1', '3240.fx1', '3240.fy1', '4860.k1', '4860.n1', '4860.x1', '4860.bm1', '4860.bn1', '4860.bz1', '4860.ce1'], 'contains': ['19440.n1', '19440.o1', '19440.u1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [443120025600, 180667423197, 442641341252], 'label': '77760.bo.9720.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '9720.bt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.bt1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056765
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.co2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.fs1', '3240.fz1', '3240.ga1', '4860.k1', '4860.ba1', '4860.br1', '4860.bt1', '4860.ca1'], 'contains': ['19440.n1', '19440.p1', '19440.q1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [375138087093, 482631093, 87181920000], 'label': '77760.bo.9720.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '9720.bu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.bu1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056766
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3240.ft1', '3240.gb1', '3240.gf1', '4860.i1', '4860.y1', '4860.bt1', '4860.cb1'], 'contains': ['19440.n2', '19440.q1', '19440.s1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [19678982400, 7185024000, 462320369015], 'label': '77760.bo.9720.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '9720.bv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.bv1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056767
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3240.fu1', '3240.gc1', '3240.gg1', '4860.j1', '4860.y1', '4860.bv1', '4860.cc1', '4860.ci1'], 'contains': ['19440.n2', '19440.r1', '19440.v1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [19678982400, 462320185080, 7185202680], 'label': '77760.bo.9720.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '9720.bw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.bw1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056768
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.fv1', '3240.gd1', '3240.ge1', '4860.i1', '4860.j1', '4860.z1', '4860.bm2', '4860.ce1'], 'contains': ['19440.n2', '19440.t1', '19440.u1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [7185207845, 19678982400, 462320149704], 'label': '77760.bo.9720.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '9720.bx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.bx1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056769
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.co2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.ie1', '3240.fw1', '3240.gh1', '3240.gi1', '4860.l1', '4860.bb1', '4860.br1', '4860.bz1', '4860.ci1'], 'contains': ['19440.n1', '19440.r1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [87261753600, 456053069398, 83462998], 'label': '77760.bo.9720.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '9720.by1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.by1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056770
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.gj1', '3240.gl1', '3240.gm1', '4860.m1', '4860.p1', '4860.bk1', '4860.bm1', '4860.bm2', '4860.bo1', '4860.ca1'], 'contains': ['19440.o1', '19440.p1', '19440.t1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [355938191405, 374659084800, 87182282615], 'label': '77760.bo.9720.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '9720.bz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.bz1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056771
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.e1', '30.c1', '40.b1', '60.o1'], 'contains': ['240.e1', '240.h1', '240.i1', '240.bf1', '240.bj1', '240.bq1', '240.bt1', '360.k1', '360.bc1', '360.be1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [143975, 80787, 519235320, 442641386424, 998144375, 183845, 80880], 'label': '77760.bo.120.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '120.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.j1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246056772
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.ck2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.gk1', '3240.go1', '3240.gq1', '4860.m1', '4860.q1', '4860.bh1', '4860.bp1', '4860.bu1', '4860.bz1', '4860.cc1'], 'contains': ['19440.o1', '19440.r1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [87182277597, 355938463197, 374659084800], 'label': '77760.bo.9720.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '9720.ca1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.ca1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056773
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.r2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.gn1', '3240.gp1', '4860.p1', '4860.bh1', '4860.bn1', '4860.bq1', '4860.cb1'], 'contains': ['19440.o1', '19440.s1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [87182277597, 374659084800, 355938191305], 'label': '77760.bo.9720.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '9720.cb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.cb1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056774
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.co2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3240.gr1', '3240.gs1', '3240.gt1', '4860.m1', '4860.bl1', '4860.br1', '4860.bv1', '4860.cd1'], 'contains': ['19440.p1', '19440.r1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [374659084800, 355938468215, 87182282615], 'label': '77760.bo.9720.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '9720.cc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.cc1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056775
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.ck2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.gu1', '3240.gy1', '3240.gz1', '3240.ha1', '3240.hb1', '3240.hc1', '4860.f1', '4860.n1', '4860.bi1', '4860.bw1', '4860.ce1', '4860.cg1', '4860.ch1'], 'contains': ['19440.m1', '19440.u1', '19440.w1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [482630400, 375138172555, 87181920000], 'label': '77760.bo.9720.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '9720.cd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.cd1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056776
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bd1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.gv1', '3240.gw1', '3240.gx1', '3240.hd1', '3240.he1', '4860.h1', '4860.o1', '4860.bj1', '4860.bs1', '4860.cf1', '4860.cg1', '4860.ch1'], 'contains': ['19440.m1', '19440.m2', '19440.w1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [19678982400, 448908284158, 462320328958], 'label': '77760.bo.9720.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '9720.ce1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.ce1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056777
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.co2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.hf1', '3240.hj1', '3240.hk1', '3240.hl1', '3240.hm1', '3240.hn1', '4860.n1', '4860.ba1', '4860.bx1', '4860.cf1', '4860.ci1'], 'contains': ['19440.n1', '19440.v1', '19440.w1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [375138087093, 482630400, 87181920000], 'label': '77760.bo.9720.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '9720.cf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.cf1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056778
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.hg1', '3240.hh1', '3240.hi1', '3240.ho1', '3240.hp1', '4860.o1', '4860.bc1', '4860.bt1', '4860.ce1', '4860.ci1'], 'contains': ['19440.n1', '19440.n2', '19440.w1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [461841004800, 19678982400, 462320369015], 'label': '77760.bo.9720.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '9720.cg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.cg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056779
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.ck2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.hq1', '3240.hr1', '3240.hs1', '3240.ht1', '3240.hu1', '3240.hv1', '4860.p1', '4860.q1', '4860.bk1', '4860.bs1', '4860.bw1', '4860.ce1', '4860.cf1'], 'contains': ['19440.o1', '19440.t1', '19440.w1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [87181925066, 374659084800, 355938105600], 'label': '77760.bo.9720.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '9720.ch1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.ch1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056780
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.co2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.hw1', '3240.hx1', '3240.hy1', '3240.hz1', '3240.ia1', '3240.ib1', '4860.p1', '4860.bl1', '4860.bt1', '4860.bx1', '4860.cg1'], 'contains': ['19440.p1', '19440.s1', '19440.w1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [374659084800, 355938105600, 87182282615], 'label': '77760.bo.9720.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '9720.ci1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.ci1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056781
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '9720.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.bv2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3240.ic1', '3240.id1', '3240.ie1', '3240.if1', '4860.q1', '4860.bl1', '4860.by1', '4860.ch1', '4860.ci1'], 'contains': ['19440.r1', '19440.w1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [374659084800, 355938105600, 87181920000], 'label': '77760.bo.9720.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '9720.cj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9720.cj1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 246056782
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.b1', '60.f1', '60.g1', '60.m1'], 'contains': ['240.g1', '240.j1', '240.bk1', '240.br1', '240.bx1', '360.l1', '360.m1', '360.be1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [180587277504, 93448857748, 174400173363, 456053073961, 85805, 80880, 80787], 'label': '77760.bo.120.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '120.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.k1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246056783
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.a1', '4320.b1', '4320.e1', '6480.a1', '6480.e1', '6480.h1', '6480.k1', '6480.w1'], 'contains': ['25920.b1', '38880.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [183845, 80880], 'label': '77760.bo.12960.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1440.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '12960.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056784
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.v1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.o1', '4320.b1', '4320.c1', '4320.d1', '4320.f1', '4320.h1', '6480.b1', '6480.d1', '6480.f1', '6480.g1', '6480.i1', '6480.l1', '6480.n1'], 'contains': ['25920.d1', '38880.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [183845, 355419187200], 'label': '77760.bo.12960.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '12960.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056786
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.b1', '4320.a1', '4320.e1', '4320.f1', '4320.g1', '6480.o1', '6480.q1', '6480.t1', '6480.v1', '6480.x1'], 'contains': ['25920.a1', '38880.a1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [183845, 80787], 'label': '77760.bo.12960.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1440.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12960.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056787
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.c1', '4320.a1', '4320.h1', '6480.p1', '6480.r1', '6480.s1', '6480.u1', '6480.w1'], 'contains': ['25920.b1', '38880.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [183845, 143975], 'label': '77760.bo.12960.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1440.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '12960.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056788
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.d1', '4320.i1', '4320.l1', '4320.m1', '6480.x1', '6480.y1', '6480.bc1', '6480.bf1', '6480.bi1'], 'contains': ['25920.a1', '38880.b1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [80787, 143304], 'label': '77760.bo.12960.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1440.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '12960.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056789
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.cd1', '4320.i1', '4320.j1', '4320.k1', '4320.n1', '4320.p1', '6480.n1', '6480.z1', '6480.bb1', '6480.bd1', '6480.be1', '6480.bg1', '6480.bj1'], 'contains': ['25920.d1', '38880.b1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [355419504452, 317252], 'label': '77760.bo.12960.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.r1', 'old_label': '12960.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056790
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.bm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.ce1', '4320.i1', '4320.j1', '4320.o1', '4320.q1', '6480.ba1', '6480.bh1', '6480.bk1'], 'contains': ['25920.e1', '38880.b1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [355419549955, 317252], 'label': '77760.bo.12960.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.bu1', 'old_label': '12960.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056791
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.e1', '4320.l1', '4320.n1', '4320.o1', '6480.w1', '6480.bl1', '6480.bn1', '6480.bp1', '6480.bq1'], 'contains': ['25920.b1', '38880.b1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [143975, 143304], 'label': '77760.bo.12960.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1440.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12960.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.i1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056792
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.f1', '4320.m1', '4320.p1', '4320.q1', '6480.bm1', '6480.bo1'], 'contains': ['25920.c1', '38880.b1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [143731, 143304], 'label': '77760.bo.12960.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1440.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '12960.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.j1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056793
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.f1', '30.d1', '40.c1', '60.o1'], 'contains': ['240.i1', '240.m1', '240.n1', '240.bt1', '240.bu1', '240.ch1', '240.ck1', '360.n1', '360.bf1', '360.bl1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [183845, 368871287518, 174436599746, 143975, 375138270474, 80880, 80787], 'label': '77760.bo.120.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '120.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.l1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246056794
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '30.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4320.r1', '4320.s1', '4320.t1', '4320.u1', '4320.v1', '4320.ba1', '6480.o1', '6480.y1', '6480.bs1', '6480.bs2', '6480.bx1', '6480.bx2', '6480.cd1', '6480.cd2'], 'contains': ['25920.a1', '38880.c1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [80787, 375138086400], 'label': '77760.bo.12960.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '12960.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056795
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '90.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4320.r1', '4320.w1', '4320.x1', '4320.bb1', '6480.a1', '6480.p1', '6480.bl1', '6480.br1', '6480.br2', '6480.bt1', '6480.bt2', '6480.by1', '6480.by2', '6480.ce1', '6480.ce2'], 'contains': ['25920.b1', '38880.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [442641386187, 143975], 'label': '77760.bo.12960.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '12960.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.l1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056796
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.ef1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4320.s1', '4320.y1', '4320.z1', '4320.bc1', '6480.bm1', '6480.bz1', '6480.bz2', '6480.cf1', '6480.cf2'], 'contains': ['25920.c1', '38880.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [442641386284, 179159], 'label': '77760.bo.12960.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '12960.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.m1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056797
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.ee1', '4320.t1', '4320.w1', '4320.y1', '4320.bg1', '6480.b1', '6480.z1', '6480.bu1', '6480.ca1', '6480.ci1'], 'contains': ['25920.d1', '38880.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [518918400, 442641024000], 'label': '77760.bo.12960.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '12960.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056798
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '240.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.ef1', '4320.t1', '4320.x1', '4320.z1', '4320.bd1', '6480.ba1', '6480.bv1'], 'contains': ['25920.e1', '38880.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [174436496787, 375138086400], 'label': '77760.bo.12960.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.bc1', 'old_label': '12960.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.o1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056799
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.eg1', '4320.u1', '4320.w1', '4320.x1', '4320.be1', '6480.c1', '6480.bw1', '6480.cb1'], 'contains': ['25920.f1', '38880.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [518963904, 442641024000], 'label': '77760.bo.12960.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.f1', 'old_label': '12960.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.p1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056800
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.eh1', '4320.v1', '4320.y1', '4320.z1', '4320.bf1', '6480.cc1'], 'contains': ['25920.g1', '38880.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [174436640612, 375138086400], 'label': '77760.bo.12960.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '720.cu1', 'old_label': '12960.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.q1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056801
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.ei1', '4320.ba1', '4320.bb1', '4320.bc1', '4320.bd1', '4320.be1', '4320.bf1', '4320.bg1', '6480.d1', '6480.bb1', '6480.cg1', '6480.ch1', '6480.ci1'], 'contains': ['25920.d1', '38880.c1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [188331091200, 375138086400], 'label': '77760.bo.12960.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '12960.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.r1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056802
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '90.bi1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.g1', '4320.bh1', '4320.bi1', '4320.bj1', '6480.q1', '6480.bc1', '6480.cd1', '6480.cd2', '6480.ck1', '6480.ck2', '6480.cm1', '6480.cm2', '6480.cq1', '6480.cs1', '6480.cv1', '6480.cw1', '6480.cx1', '6480.cy1', '6480.cz1', '6480.da1', '6480.dp1'], 'contains': ['25920.a1', '38880.d1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [274467962404, 80787], 'label': '77760.bo.12960.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '12960.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.s1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056803
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '270.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.h1', '4320.bh1', '4320.bk1', '6480.e1', '6480.r1', '6480.bn1', '6480.ce1', '6480.ce2', '6480.cj1', '6480.cj2', '6480.cl1', '6480.cl2', '6480.cn1', '6480.cn2', '6480.cp1', '6480.cr1', '6480.ct1', '6480.db1', '6480.dc1', '6480.dd1', '6480.de1', '6480.df1', '6480.dg1', '6480.dh1', '6480.di1', '6480.dq1'], 'contains': ['25920.b1', '38880.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [274467997680, 80880], 'label': '77760.bo.12960.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '12960.t1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.t1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056804
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.b1', '60.d1', '60.e1', '60.h1', '60.i1', '60.j1', '60.l1', '60.p1'], 'contains': ['240.bv1', '360.o1', '360.bm1', '360.bn1', '360.bo1', '480.d1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [143975, 80787, 442681079189, 355419504028, 183845, 80880, 355499026316], 'label': '77760.bo.120.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '120.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.m1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246056956
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '162.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['27.a1', '54.d1', '54.e1'], 'contains': ['324.a1', '324.b1', '324.c1', '324.f1', '324.g1', '810.m1', '972.a1', '1620.ba1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [362615, 443555839197, 5066, 479001600], 'label': '77760.bo.162.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '162.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.a1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
  • id: 246056805
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.fz1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.i1', '4320.bi1', '4320.bl1', '6480.bo1', '6480.cf1', '6480.cf2', '6480.co1', '6480.co2', '6480.cu1', '6480.dj1', '6480.dk1', '6480.dl1', '6480.dm1', '6480.dr1'], 'contains': ['25920.c1', '38880.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [274467916800, 179159], 'label': '77760.bo.12960.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '12960.u1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.u1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056806
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.bs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.w1', '3240.if1', '4320.bj1', '4320.bk1', '4320.bl1', '4320.bm1', '6480.f1', '6480.bd1', '6480.ci1', '6480.dn1', '6480.do1'], 'contains': ['25920.d1', '38880.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [113566924800, 88176211200], 'label': '77760.bo.12960.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '12960.v1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.v1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056807
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '270.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4320.bn1', '4320.bo1', '4320.br1', '4320.bt1', '6480.a1', '6480.s1', '6480.bp1', '6480.br1', '6480.br2', '6480.cj1', '6480.cj2', '6480.dw1', '6480.dw2', '6480.ed1', '6480.ed2'], 'contains': ['25920.b1', '38880.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [45363, 442641300958], 'label': '77760.bo.12960.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '12960.w1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.w1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056808
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.bi1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.gw1', '4320.bn1', '4320.bp1', '4320.bs1', '4320.bu1', '4320.bv1', '4320.bx1', '6480.b1', '6480.g1', '6480.be1', '6480.cg1', '6480.dn1', '6480.dx1', '6480.ee1'], 'contains': ['25920.d1', '38880.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [375138172205, 174436416000], 'label': '77760.bo.12960.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '12960.x1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.x1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056809
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.gx1', '4320.bn1', '4320.bq1', '4320.bw1', '4320.by1', '6480.c1', '6480.dy1', '6480.ef1'], 'contains': ['25920.f1', '38880.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [519235320, 442641109705], 'label': '77760.bo.12960.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.a1', 'old_label': '12960.y1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.y1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056810
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '270.by1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4320.bo1', '4320.bp1', '4320.bq1', '4320.bz1', '4320.ca1', '4320.cb1', '6480.o1', '6480.t1', '6480.bf1', '6480.bs1', '6480.bs2', '6480.ck1', '6480.ck2', '6480.dz1', '6480.dz2', '6480.eg1', '6480.eg2'], 'contains': ['25920.a1', '38880.e1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [442641109705, 80787], 'label': '77760.bo.12960.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '12960.z1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.z1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056811
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4320.bs1', '4320.bz1', '4320.cc1', '4320.cd1', '6480.h1', '6480.p1', '6480.bp1', '6480.bt1', '6480.bt2', '6480.cl1', '6480.cl2', '6480.ec1', '6480.ec2', '6480.ed1', '6480.ed2'], 'contains': ['25920.b1', '38880.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [442641109705, 80880], 'label': '77760.bo.12960.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '12960.ba1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.ba1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056812
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.bj1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.ha1', '4320.br1', '4320.bw1', '4320.bx1', '4320.ca1', '4320.cc1', '6480.d1', '6480.i1', '6480.bg1', '6480.bu1', '6480.dn1', '6480.ea1', '6480.ee1'], 'contains': ['25920.d1', '38880.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [188331091200, 375138172555], 'label': '77760.bo.12960.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '12960.bb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.bb1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056813
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.ch1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.hb1', '4320.bt1', '4320.bu1', '4320.by1', '4320.ca1', '4320.cd1', '6480.bh1', '6480.bv1', '6480.eb1'], 'contains': ['25920.e1', '38880.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [188331171987, 375138172555], 'label': '77760.bo.12960.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.cb1', 'old_label': '12960.bc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.bc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056814
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.hc1', '4320.bv1', '4320.cb1', '4320.cc1', '4320.cd1', '6480.j1', '6480.bw1', '6480.ef1'], 'contains': ['25920.f1', '38880.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [188331136563, 375138172205], 'label': '77760.bo.12960.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.c1', 'old_label': '12960.bd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.bd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056815
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.c1', '60.f1', '60.k1', '60.m1'], 'contains': ['240.j1', '240.l1', '240.bw1', '240.by1', '240.cg1', '360.p1', '360.q1', '360.bl1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [180587277504, 456053074316, 93448857748, 174400173363, 85805, 80880, 80787], 'label': '77760.bo.120.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '120.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.n1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246056816
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '270.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4320.ce1', '4320.cf1', '4320.cg1', '4320.ch1', '4320.ci1', '4320.cj1', '6480.t1', '6480.y1', '6480.bx1', '6480.bx2', '6480.cm1', '6480.cm2', '6480.dz1', '6480.dz2'], 'contains': ['25920.a1', '38880.f1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [442641386755, 80787], 'label': '77760.bo.12960.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '12960.be1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.be1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056817
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.bl1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.hh1', '4320.ce1', '4320.ck1', '4320.cm1', '4320.cp1', '4320.cq1', '4320.cr1', '6480.g1', '6480.z1', '6480.ch1', '6480.do1', '6480.ea1'], 'contains': ['25920.d1', '38880.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [375138087093, 174436416000], 'label': '77760.bo.12960.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '12960.bf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.bf1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056818
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.bo1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.hi1', '4320.ce1', '4320.cl1', '4320.cn1', '4320.co1', '4320.cs1', '4320.ct1', '6480.ba1', '6480.eb1'], 'contains': ['25920.e1', '38880.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [174436496787, 375138087093], 'label': '77760.bo.12960.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.bz1', 'old_label': '12960.bg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.bg1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056819
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '270.p1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4320.cf1', '4320.ck1', '4320.cl1', '4320.cu1', '6480.h1', '6480.s1', '6480.bl1', '6480.by1', '6480.by2', '6480.cn1', '6480.cn2', '6480.dw1', '6480.dw2', '6480.ec1', '6480.ec2'], 'contains': ['25920.b1', '38880.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [375138087093, 148], 'label': '77760.bo.12960.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '12960.bh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.bh1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056820
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.ga1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4320.cg1', '4320.cm1', '4320.cn1', '4320.cv1', '6480.bm1', '6480.bz1', '6480.bz2', '6480.co1', '6480.co2'], 'contains': ['25920.c1', '38880.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [442641341252, 224612], 'label': '77760.bo.12960.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '12960.bi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.bi1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056821
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.bm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.hl1', '4320.ch1', '4320.co1', '4320.cr1', '4320.cu1', '4320.cv1', '6480.i1', '6480.bb1', '6480.ca1', '6480.do1', '6480.dx1'], 'contains': ['25920.d1', '38880.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [375138087093, 188331091200], 'label': '77760.bo.12960.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.r1', 'old_label': '12960.bj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.bj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056822
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.s1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.hm1', '4320.ci1', '4320.cp1', '4320.cs1', '4320.cu1', '6480.j1', '6480.cb1', '6480.dy1'], 'contains': ['25920.f1', '38880.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [375138087093, 188331091348], 'label': '77760.bo.12960.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.i1', 'old_label': '12960.bk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.bk1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056823
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.hn1', '4320.cj1', '4320.cq1', '4320.ct1', '4320.cv1', '6480.cc1'], 'contains': ['25920.g1', '38880.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [442162247012, 442641341252], 'label': '77760.bo.12960.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '720.di1', 'old_label': '12960.bl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.bl1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246057087
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.d1', '9.a1'], 'contains': ['36.f1', '36.s1', '36.w1', '54.b1', '108.g1', '180.m1', '270.s1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [462320363525, 138242, 143975, 93924236159], 'label': '77760.bo.18.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
  • id: 246056824
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.j1', '4320.cw1', '4320.cx1', '4320.cy1', '6480.e1', '6480.u1', '6480.bq1', '6480.br1', '6480.br2', '6480.cp1', '6480.ec1', '6480.ec2', '6480.eh1'], 'contains': ['25920.b1', '38880.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [274468100401, 80880], 'label': '77760.bo.12960.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '12960.bm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.bm1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056825
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.k1', '4320.cw1', '4320.cz1', '4320.da1', '4320.db1', '6480.q1', '6480.v1', '6480.bi1', '6480.bs1', '6480.bs2', '6480.cq1', '6480.dz1', '6480.dz2', '6480.ei1'], 'contains': ['25920.a1', '38880.g1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [274468135825, 80787], 'label': '77760.bo.12960.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '12960.bn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.bn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056826
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '40.d1', '60.g1', '60.k1', '60.n1'], 'contains': ['240.j1', '240.ca1', '240.cd1', '360.r1', '360.t1', '1080.bs1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [183845, 482849425, 143975, 193999455812, 280259665445, 80787, 88695348625], 'label': '77760.bo.120.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '120.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.o1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246056827
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.l1', '4320.cz1', '4320.dc1', '4320.dd1', '6480.k1', '6480.r1', '6480.bq1', '6480.bt1', '6480.bt2', '6480.cr1', '6480.dw1', '6480.dw2', '6480.eh1'], 'contains': ['25920.b1', '38880.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [274468002505, 80880], 'label': '77760.bo.12960.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '12960.bo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.bo1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056828
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.ht1', '4320.cx1', '4320.da1', '4320.dc1', '4320.de1', '4320.df1', '4320.dg1', '6480.f1', '6480.l1', '6480.bj1', '6480.bu1', '6480.cg1', '6480.dx1', '6480.ea1'], 'contains': ['25920.d1', '38880.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [368392152509, 442637395200], 'label': '77760.bo.12960.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '12960.bp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.bp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056829
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.hu1', '4320.cy1', '4320.da1', '4320.dd1', '4320.de1', '4320.dh1', '6480.bk1', '6480.bv1', '6480.eb1'], 'contains': ['25920.e1', '38880.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [442637475987, 368392188092], 'label': '77760.bo.12960.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.cm1', 'old_label': '12960.bq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.bq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056830
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.hv1', '4320.db1', '4320.dc1', '4320.dd1', '4320.df1', '4320.dh1', '6480.m1', '6480.bw1', '6480.dy1'], 'contains': ['25920.f1', '38880.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 12960, 'diagramx': None, 'generators': [368392152509, 442637476080], 'label': '77760.bo.12960.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3240.c1', 'old_label': '12960.br1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.br1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056831
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.m1', '4320.di1', '4320.dj1', '4320.dk1', '4320.dl1', '4320.dm1', '6480.v1', '6480.bc1', '6480.bx1', '6480.bx2', '6480.cs1', '6480.eg1', '6480.eg2', '6480.ei1'], 'contains': ['25920.a1', '38880.h1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [274468060348, 80787], 'label': '77760.bo.12960.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '12960.bs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.bs1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056832
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.n1', '4320.di1', '4320.dn1', '6480.k1', '6480.u1', '6480.bn1', '6480.by1', '6480.by2', '6480.ct1', '6480.ed1', '6480.ed2', '6480.eh1'], 'contains': ['25920.b1', '38880.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [179012, 274468095480], 'label': '77760.bo.12960.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '12960.bt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.bt1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056833
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.o1', '4320.dj1', '4320.do1', '6480.bo1', '6480.bz1', '6480.bz2', '6480.cu1'], 'contains': ['25920.c1', '38880.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [274468095480, 179159], 'label': '77760.bo.12960.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '12960.bu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.bu1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056834
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.hz1', '4320.dk1', '4320.dn1', '4320.do1', '4320.dp1', '4320.dq1', '4320.dr1', '6480.l1', '6480.bd1', '6480.ca1', '6480.ch1', '6480.ee1'], 'contains': ['25920.d1', '38880.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [113566924800, 88176211650], 'label': '77760.bo.12960.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '12960.bv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.bv1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056835
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3240.ia1', '4320.dl1', '4320.dn1', '4320.dp1', '6480.m1', '6480.cb1', '6480.ef1'], 'contains': ['25920.f1', '38880.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [442637712120, 368392147650], 'label': '77760.bo.12960.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.q1', 'old_label': '12960.bw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.bw1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056836
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12960.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3240.ib1', '4320.dm1', '4320.do1', '4320.dq1', '6480.cc1'], 'contains': ['25920.g1', '38880.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4320, 'diagramx': None, 'generators': [88176211650, 113567068531], 'label': '77760.bo.12960.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2160.dg1', 'old_label': '12960.bx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.bx1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056837
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': ['6480.u1', '6480.eh1', '6480.k1', '6480.m1', '6480.bq1', '6480.w1', '6480.by1', '6480.bz1', '6480.bl1', '6480.bm1', '6480.by2', '6480.bz2', '6480.cb1', '6480.cc1', '6480.ec1', '6480.ec2', '6480.h1', '6480.j1', '6480.p1', '6480.bt1', '6480.bt2', '6480.bw1'], 'conjugacy_class_count': 2, 'contained_in': ['4.d1', '6.a1', '6.c1', '6.i1'], 'contains': ['24.a1', '36.t1', '36.u1', '72.n1', '120.bz1', '180.ez1'], 'core': '12.c1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [143975, 93924409412, 462320328958, 80787], 'label': '77760.bo.12.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': ['4.d1', '6.a1'], 'normal_contains': ['24.a1'], 'normalizer': '1.a1', 'old_label': '12.c1', 'projective_image': '77760.bo', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.c1', 'subgroup_fusion': None, 'weyl_group': '77760.bo'}
  • id: 246056838
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.e1', '60.f1', '60.n1'], 'contains': ['240.j1', '240.cb1', '240.cc1', '360.s1', '360.u1', '1080.bt1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [183845, 482849425, 88695170185, 143975, 193999455812, 280259665445, 80787], 'label': '77760.bo.120.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '120.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.p1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246056839
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '15552.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5184.a1', '5184.b1', '5184.c1', '7776.a1', '7776.b1', '7776.c1', '7776.d1', '7776.e1'], 'contains': ['77760.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18764524800], 'label': '77760.bo.15552.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '15552.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15552.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 246056840
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '135.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6480.a1', '6480.b1', '6480.c1', '6480.d1', '6480.o1', '6480.p1', '9720.a1', '9720.a2', '9720.b1', '9720.b2', '9720.j1'], 'contains': ['38880.a1', '38880.c1', '38880.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [183845, 442641024000], 'label': '77760.bo.19440.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '19440.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056841
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '405.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3888.a1', '6480.e1', '6480.f1', '6480.q1', '6480.r1', '9720.b1', '9720.b2', '9720.c1', '9720.c2', '9720.d1', '9720.e1', '9720.f1', '9720.g1', '9720.h1', '9720.i1', '9720.k1'], 'contains': ['38880.a1', '38880.d1', '38880.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [274467916800, 85805], 'label': '77760.bo.19440.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '19440.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056842
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '405.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6480.g1', '6480.h1', '6480.i1', '6480.j1', '6480.s1', '6480.t1', '9720.a1', '9720.a2', '9720.c1', '9720.c2', '9720.j1'], 'contains': ['38880.a1', '38880.e1', '38880.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [5309, 442641341252], 'label': '77760.bo.19440.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '19440.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056843
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1215.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3888.b1', '6480.k1', '6480.l1', '6480.m1', '6480.u1', '6480.v1', '9720.a1', '9720.a2', '9720.h1', '9720.k1'], 'contains': ['38880.a1', '38880.g1', '38880.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [183845, 274468095480], 'label': '77760.bo.19440.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '19440.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056844
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.c1', '6480.n1', '6480.w1', '6480.x1', '9720.j1', '9720.k1'], 'contains': ['38880.a1', '38880.b1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [85805, 143304], 'label': '77760.bo.19440.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '720.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '19440.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056845
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '135.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6480.y1', '6480.z1', '6480.ba1', '6480.bb1', '6480.bl1', '6480.bm1', '9720.j1', '9720.l1', '9720.l2', '9720.m1', '9720.m2'], 'contains': ['38880.b1', '38880.c1', '38880.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [442641024000, 143304], 'label': '77760.bo.19440.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '19440.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056846
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '405.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.d1', '6480.bc1', '6480.bd1', '6480.bn1', '6480.bo1', '9720.k1', '9720.m1', '9720.m2', '9720.n1', '9720.n2', '9720.o1', '9720.p1', '9720.q1', '9720.r1', '9720.s1', '9720.t1'], 'contains': ['38880.b1', '38880.d1', '38880.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [274467916800, 143304], 'label': '77760.bo.19440.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '19440.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056847
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '405.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6480.be1', '6480.bf1', '6480.bg1', '6480.bh1', '6480.bp1', '9720.j1', '9720.l1', '9720.l2', '9720.n1', '9720.n2'], 'contains': ['38880.b1', '38880.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [178680, 442641109705], 'label': '77760.bo.19440.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '19440.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056848
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1215.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.e1', '6480.bi1', '6480.bj1', '6480.bk1', '6480.bq1', '9720.k1', '9720.l1', '9720.l2', '9720.o1'], 'contains': ['38880.b1', '38880.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1215, 'diagramx': None, 'generators': [178680, 274468002505], 'label': '77760.bo.19440.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '19440.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056849
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.f1', '60.m1'], 'contains': ['240.a1', '240.c1', '240.g1', '240.l1', '240.r1', '240.t1', '240.x1', '360.v1', '360.x1', '360.bp1', '360.bq1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [93448857748, 83543730, 174400173363, 85805, 80880, 80787, 693], 'label': '77760.bo.120.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '120.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.q1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 246056850
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bd1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6480.br1', '6480.bs1', '6480.bt1', '6480.bu1', '6480.bv1', '6480.bw1', '6480.cg1', '9720.a1', '9720.b1', '9720.l1', '9720.u1', '9720.u3', '9720.v1', '9720.v2'], 'contains': ['38880.c1', '38880.e1', '38880.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': None, 'generators': [442641024000, 443120066492], 'label': '77760.bo.19440.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bd1', 'old_label': '19440.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056851
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.j2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '405.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6480.br2', '6480.bs2', '6480.bt2', '9720.a2', '9720.b2', '9720.l2', '9720.u1', '9720.u2', '9720.v1', '9720.v2'], 'contains': ['38880.c1', '38880.e1', '38880.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [448907961600, 442641301050], 'label': '77760.bo.19440.j2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '19440.j2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.j2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056852
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6480.bx1', '6480.by1', '6480.bz1', '6480.ca1', '6480.cb1', '6480.cc1', '6480.ch1', '9720.a1', '9720.m1', '9720.u1', '9720.x1', '9720.x2'], 'contains': ['38880.c1', '38880.f1', '38880.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [87182282615, 375138086400], 'label': '77760.bo.19440.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.bi1', 'old_label': '19440.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056853
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.k2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '405.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6480.bx2', '6480.by2', '6480.bz2', '9720.a2', '9720.m2', '9720.u2', '9720.u3', '9720.x1', '9720.x2'], 'contains': ['38880.c1', '38880.f1', '38880.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [442641024000, 448908243571], 'label': '77760.bo.19440.k2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '19440.k2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.k2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056854
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '90.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6480.cd1', '6480.ce1', '6480.cf1', '6480.ci1', '9720.b1', '9720.m1', '9720.v2', '9720.w1', '9720.x2', '9720.y1', '9720.z1', '9720.ba1', '9720.be1', '9720.bf1', '9720.bg1'], 'contains': ['38880.c1', '38880.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [375138086400, 87181920000], 'label': '77760.bo.19440.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '19440.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.l1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056855
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.l2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '45.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6480.cd2', '6480.ce2', '6480.cf2', '9720.b2', '9720.m2', '9720.v1', '9720.x1', '9720.bb1', '9720.bc1', '9720.bd1', '9720.bg1'], 'contains': ['38880.c1', '38880.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [448907961600, 442641024000], 'label': '77760.bo.19440.l2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '19440.l2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.l2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056856
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bd1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6480.cj1', '6480.ck1', '6480.cl1', '6480.dn1', '9720.b1', '9720.c1', '9720.n1', '9720.v1', '9720.w1', '9720.bh2', '9720.bi1', '9720.bj1', '9720.bk1', '9720.bl1', '9720.bq1', '9720.br1', '9720.bs1', '9720.cd1', '9720.ce1'], 'contains': ['38880.d1', '38880.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [443120025600, 442641301050], 'label': '77760.bo.19440.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '19440.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.m1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056857
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.m2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '405.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6480.cj2', '6480.ck2', '6480.cl2', '9720.b2', '9720.c2', '9720.n2', '9720.v2', '9720.bh1', '9720.bm1', '9720.bn1', '9720.bo1', '9720.bp1', '9720.bq1', '9720.ce1'], 'contains': ['38880.d1', '38880.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [442641064349, 448908001949], 'label': '77760.bo.19440.m2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '19440.m2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.m2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056858
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6480.cm1', '6480.cn1', '6480.co1', '6480.do1', '9720.c1', '9720.m1', '9720.x1', '9720.y1', '9720.bh1', '9720.bi1', '9720.bt1', '9720.bu1', '9720.by1', '9720.cf1', '9720.cg1'], 'contains': ['38880.d1', '38880.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [375138087093, 87181920000], 'label': '77760.bo.19440.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '19440.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056859
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.n2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '405.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6480.cm2', '6480.cn2', '6480.co2', '9720.c2', '9720.m2', '9720.x2', '9720.bh2', '9720.bv1', '9720.bw1', '9720.bx1', '9720.cg1'], 'contains': ['38880.d1', '38880.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [442641305971, 448908243571], 'label': '77760.bo.19440.n2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '19440.n2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.n2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056860
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.g1', '60.m1', '60.n1'], 'contains': ['240.b1', '240.d1', '240.j1', '240.p1', '240.r1', '240.v1', '240.y1', '360.w1', '360.y1', '360.br1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [280259521949, 193999455627, 482768881, 85805, 80880, 80787, 143304], 'label': '77760.bo.120.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '120.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.r1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246056861
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bd1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6480.cp1', '6480.cq1', '6480.cr1', '9720.h1', '9720.i1', '9720.o1', '9720.v1', '9720.v2', '9720.z1', '9720.bh1', '9720.bh2', '9720.bj1', '9720.bk1', '9720.bt1', '9720.bz1', '9720.ca1', '9720.cb1', '9720.ch1'], 'contains': ['38880.d1', '38880.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': None, 'generators': [442681124645, 355499204645], 'label': '77760.bo.19440.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '19440.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.o1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056862
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6480.cs1', '6480.ct1', '6480.cu1', '9720.h1', '9720.t1', '9720.x1', '9720.x2', '9720.ba1', '9720.bl1', '9720.bq1', '9720.bu1', '9720.bz1', '9720.cc1', '9720.ci1'], 'contains': ['38880.d1', '38880.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [442681119480, 355499020800], 'label': '77760.bo.19440.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '19440.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.p1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056863
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '90.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.f1', '6480.cv1', '6480.db1', '6480.dj1', '9720.d1', '9720.p1', '9720.bb1', '9720.be1', '9720.bj1', '9720.bm1', '9720.bu1', '9720.bv1'], 'contains': ['38880.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [443120025600, 267845356800], 'label': '77760.bo.19440.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '19440.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.q1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056864
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '90.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.fm1', '6480.cw1', '6480.dc1', '6480.dk1', '9720.e1', '9720.q1', '9720.bb1', '9720.bf1', '9720.bn1', '9720.br1', '9720.bw1', '9720.by1', '9720.ca1', '9720.cc1', '9720.cj1'], 'contains': ['38880.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [88695129600, 482630400], 'label': '77760.bo.19440.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '19440.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.r1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056865
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.fn1', '6480.cx1', '6480.dd1', '6480.dl1', '9720.f1', '9720.q1', '9720.y1', '9720.bc1', '9720.bo1', '9720.bs1', '9720.bv1', '9720.cb1', '9720.ci1'], 'contains': ['38880.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [482630400, 88695272904], 'label': '77760.bo.19440.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '19440.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.s1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056866
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2160.fo1', '6480.cy1', '6480.de1', '6480.df1', '9720.e1', '9720.f1', '9720.r1', '9720.w1', '9720.bd1', '9720.bi1', '9720.bm1', '9720.bp1', '9720.bx1', '9720.bz1', '9720.ch1'], 'contains': ['38880.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [88695170185, 482630400], 'label': '77760.bo.19440.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '19440.t1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.t1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056867
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3888.g1', '6480.cz1', '6480.dg1', '6480.dh1', '9720.d1', '9720.g1', '9720.s1', '9720.z1', '9720.bd1', '9720.bl1', '9720.bn1', '9720.bo1', '9720.bt1', '9720.bx1', '9720.cd1'], 'contains': ['38880.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [443120025600, 267845397242], 'label': '77760.bo.19440.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '19440.u1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.u1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056868
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.h1', '6480.da1', '6480.di1', '6480.dm1', '9720.g1', '9720.p1', '9720.ba1', '9720.bc1', '9720.bk1', '9720.bp1', '9720.bw1', '9720.cf1'], 'contains': ['38880.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [443120025600, 267845674052], 'label': '77760.bo.19440.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '19440.v1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.v1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056869
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '90.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6480.dp1', '6480.dq1', '6480.dr1', '6480.ds1', '6480.dt1', '6480.du1', '6480.dv1', '9720.i1', '9720.t1', '9720.be1', '9720.bg1', '9720.cd1', '9720.ce1', '9720.cf1', '9720.cg1', '9720.ch1', '9720.ci1', '9720.cj1'], 'contains': ['38880.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [274467916800, 268244524800], 'label': '77760.bo.19440.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '19440.w1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.w1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 246056870
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6480.dw1', '6480.dx1', '6480.dy1', '6480.dz1', '6480.ea1', '6480.eb1', '6480.ec1', '9720.a1', '9720.c1', '9720.l1', '9720.u1', '9720.u2', '9720.bh1', '9720.bh2'], 'contains': ['38880.e1', '38880.f1', '38880.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 9720, 'diagramx': None, 'generators': [375138172555, 87182005805], 'label': '77760.bo.19440.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2430.j1', 'old_label': '19440.x1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.x1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056871
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['30.f1', '40.f1', '60.o1'], 'contains': ['240.e1', '240.m1', '240.s1', '240.z1', '240.bc1', '360.bp1', '360.bs1'], 'core': '720.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [174436599746, 143975, 375138270474, 85805, 80880, 80787, 143304], 'label': '77760.bo.120.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '120.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.s1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246056872
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.x2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1215.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6480.dw2', '6480.dz2', '6480.ec2', '9720.a2', '9720.c2', '9720.l2', '9720.u1', '9720.u3', '9720.bh1', '9720.bh2'], 'contains': ['38880.e1', '38880.f1', '38880.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [442641109946, 448908243571], 'label': '77760.bo.19440.x2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '19440.x2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.x2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056873
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6480.ed1', '6480.ee1', '6480.ef1', '6480.eg1', '9720.a1', '9720.n1', '9720.u2', '9720.u3', '9720.bq1'], 'contains': ['38880.e1', '38880.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [375138172205, 87182282615], 'label': '77760.bo.19440.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2430.j1', 'old_label': '19440.y1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.y1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056874
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.y2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1215.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6480.ed2', '6480.eg2', '9720.a2', '9720.n2', '9720.u1', '9720.bq1'], 'contains': ['38880.e1', '38880.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2430, 'diagramx': None, 'generators': [448908001949, 442641381597], 'label': '77760.bo.19440.y2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1215.a1', 'old_label': '19440.y2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.y2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056875
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '19440.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2430.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6480.eh1', '6480.ei1', '9720.h1', '9720.o1', '9720.u1', '9720.u2', '9720.u3'], 'contains': ['38880.g1', '38880.h1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 4860, 'diagramx': None, 'generators': [442681124645, 355499061149], 'label': '77760.bo.19440.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2430.j1', 'old_label': '19440.z1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19440.z1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056876
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '25920.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['5184.a1', '8640.a1', '8640.b1', '8640.c1', '8640.d1', '8640.e1', '12960.d1', '12960.f1', '12960.k1', '12960.s1', '12960.z1', '12960.be1', '12960.bn1', '12960.bs1'], 'contains': ['77760.a1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [80787], 'label': '77760.bo.25920.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '25920.a1', 'normal_contained_in': ['72.a1', '8640.a1'], 'normal_contains': ['77760.a1'], 'normalizer': '1.a1', 'old_label': '25920.a1', 'projective_image': '77760.bo', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12960.cn', 'quotient_action_kernel_order': 12960, 'quotient_fusion': None, 'short_label': '25920.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056877
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '25920.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['5184.b1', '8640.a1', '8640.f1', '8640.g1', '12960.a1', '12960.e1', '12960.i1', '12960.l1', '12960.t1', '12960.w1', '12960.ba1', '12960.bh1', '12960.bm1', '12960.bo1', '12960.bt1'], 'contains': ['77760.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [143975], 'label': '77760.bo.25920.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2880.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '25920.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '25920.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056878
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '25920.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5184.c1', '8640.b1', '8640.h1', '8640.i1', '12960.j1', '12960.m1', '12960.u1', '12960.bi1', '12960.bu1'], 'contains': ['77760.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [179159], 'label': '77760.bo.25920.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2880.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '25920.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '25920.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056879
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '25920.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6480.ds1', '8640.c1', '8640.f1', '8640.h1', '8640.j1', '8640.k1', '8640.l1', '8640.m1', '12960.b1', '12960.g1', '12960.n1', '12960.r1', '12960.v1', '12960.x1', '12960.bb1', '12960.bf1', '12960.bj1', '12960.bp1', '12960.bv1'], 'contains': ['77760.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [355419187200], 'label': '77760.bo.25920.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '25920.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '25920.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056880
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '25920.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '80.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6480.dt1', '8640.c1', '8640.g1', '8640.i1', '8640.j1', '8640.n1', '8640.o1', '12960.h1', '12960.o1', '12960.bc1', '12960.bg1', '12960.bq1'], 'contains': ['77760.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 80, 'diagramx': None, 'generators': [355419232804], 'label': '77760.bo.25920.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.h1', 'old_label': '25920.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '25920.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056881
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '25920.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '240.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6480.du1', '8640.d1', '8640.f1', '8640.g1', '8640.k1', '8640.n1', '12960.c1', '12960.p1', '12960.y1', '12960.bd1', '12960.bk1', '12960.br1', '12960.bw1'], 'contains': ['77760.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [194518339175], 'label': '77760.bo.25920.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1', 'old_label': '25920.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '25920.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056882
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['30.g1', '40.f1', '60.o1'], 'contains': ['240.h1', '240.n1', '240.s1', '240.ba1', '240.bd1', '360.bq1', '360.bs1'], 'core': '720.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [188331315147, 143975, 375138270474, 85805, 80880, 80787, 143304], 'label': '77760.bo.120.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '120.t1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.t1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246056883
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '25920.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '480.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6480.dv1', '8640.e1', '8640.h1', '8640.i1', '8640.l1', '8640.o1', '12960.q1', '12960.bl1', '12960.bx1'], 'contains': ['77760.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [194518374451], 'label': '77760.bo.25920.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.bp1', 'old_label': '25920.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '25920.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 246056884
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '38880.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['7776.a1', '12960.a1', '12960.b1', '12960.c1', '12960.d1', '12960.e1', '19440.a1', '19440.b1', '19440.c1', '19440.d1', '19440.e1'], 'contains': ['77760.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [183845], 'label': '77760.bo.38880.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1440.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '38880.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '38880.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056885
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '38880.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7776.b1', '12960.f1', '12960.g1', '12960.h1', '12960.i1', '12960.j1', '19440.e1', '19440.f1', '19440.g1', '19440.h1', '19440.i1'], 'contains': ['77760.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [143304], 'label': '77760.bo.38880.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1440.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '38880.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '38880.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056886
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '38880.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12960.k1', '12960.l1', '12960.m1', '12960.n1', '12960.o1', '12960.p1', '12960.q1', '12960.r1', '19440.a1', '19440.f1', '19440.j1', '19440.j2', '19440.k1', '19440.k2', '19440.l1', '19440.l2'], 'contains': ['77760.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [442641024000], 'label': '77760.bo.38880.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '38880.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '38880.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056887
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '38880.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '45.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7776.c1', '12960.s1', '12960.t1', '12960.u1', '12960.v1', '19440.b1', '19440.g1', '19440.l1', '19440.l2', '19440.m1', '19440.m2', '19440.n1', '19440.n2', '19440.o1', '19440.p1', '19440.q1', '19440.r1', '19440.s1', '19440.t1', '19440.u1', '19440.v1', '19440.w1'], 'contains': ['77760.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [274467916800], 'label': '77760.bo.38880.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '38880.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '38880.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056888
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '38880.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '135.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12960.w1', '12960.x1', '12960.y1', '12960.z1', '12960.ba1', '12960.bb1', '12960.bc1', '12960.bd1', '19440.a1', '19440.c1', '19440.h1', '19440.j1', '19440.j2', '19440.m1', '19440.m2', '19440.x1', '19440.x2', '19440.y1', '19440.y2'], 'contains': ['77760.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [442641109705], 'label': '77760.bo.38880.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '38880.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '38880.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056889
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '38880.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '135.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12960.be1', '12960.bf1', '12960.bg1', '12960.bh1', '12960.bi1', '12960.bj1', '12960.bk1', '12960.bl1', '19440.c1', '19440.f1', '19440.k1', '19440.k2', '19440.n1', '19440.n2', '19440.x1', '19440.x2'], 'contains': ['77760.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [442641341252], 'label': '77760.bo.38880.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '38880.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '38880.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056890
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '38880.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '405.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['7776.d1', '12960.bm1', '12960.bn1', '12960.bo1', '12960.bp1', '12960.bq1', '12960.br1', '19440.b1', '19440.d1', '19440.i1', '19440.j1', '19440.j2', '19440.o1', '19440.x1', '19440.x2', '19440.z1'], 'contains': ['77760.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [274468135825], 'label': '77760.bo.38880.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '38880.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '38880.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056891
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '38880.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '405.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7776.e1', '12960.bs1', '12960.bt1', '12960.bu1', '12960.bv1', '12960.bw1', '12960.bx1', '19440.d1', '19440.g1', '19440.k1', '19440.k2', '19440.p1', '19440.y1', '19440.y2', '19440.z1'], 'contains': ['77760.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [274468095480], 'label': '77760.bo.38880.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '38880.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '38880.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056892
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '77760.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['15552.a1', '25920.a1', '25920.b1', '25920.c1', '25920.d1', '25920.e1', '25920.f1', '25920.g1', '38880.a1', '38880.b1', '38880.c1', '38880.d1', '38880.e1', '38880.f1', '38880.g1', '38880.h1'], 'contains': [], 'core': '77760.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [], 'label': '77760.bo.77760.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '77760.a1', 'normal_contained_in': ['216.a1', '25920.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '77760.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '77760.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 246056893
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.g1', '30.h1', '40.g1', '60.o1'], 'contains': ['240.i1', '240.q1', '240.s1', '240.bb1', '240.be1', '360.br1', '360.bt1'], 'core': '720.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [368392152811, 143975, 85805, 442637676988, 80880, 80787, 143304], 'label': '77760.bo.120.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '120.u1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.u1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246056894
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.h1', '60.m1'], 'contains': ['240.t1', '240.x1', '240.y1', '240.bi1', '240.bk1', '240.cg1', '240.cj1', '360.bu1', '360.bz1', '360.ca1', '360.cb1', '360.cc1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [174400208787, 93449036612, 224184, 143975, 456053150130, 180587272349, 80787], 'label': '77760.bo.120.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '120.v1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.v1', 'subgroup_fusion': None, 'weyl_group': '1296.3538'}
  • id: 246056895
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.i1', '60.m1', '60.q1', '60.r1'], 'contains': ['240.t1', '240.v1', '240.bm1', '240.br1', '240.by1', '360.bv1', '360.cd1', '360.cf1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [180587277504, 93448857748, 174400173363, 456053150130, 80880, 80787, 693], 'label': '77760.bo.120.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '120.w1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.w1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 246056896
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.i1', '60.s1'], 'contains': ['240.u1', '240.w1', '240.bp1', '240.bs1', '240.bz1', '360.bv1', '360.ce1', '360.cg1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [174400208787, 93449001331, 178680, 83543730, 180587232000, 80787, 179159], 'label': '77760.bo.120.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.s1', 'old_label': '120.x1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.x1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246056897
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.j1', '60.m1', '60.q1', '60.t1'], 'contains': ['240.v1', '240.x1', '240.bw1', '240.bx1', '240.cm1', '360.bw1', '360.ch1', '360.ck1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [143975, 80787, 174400208787, 143304, 93449036612, 180587232000, 456053154955], 'label': '77760.bo.120.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '120.y1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.y1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246056898
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '6.b1', '6.c1', '6.e1'], 'contains': ['24.a1', '36.b1', '36.e1', '72.b1', '120.d1', '180.o1'], 'core': '24.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [87182277125, 274511462400, 143975, 85805, 80787], 'label': '77760.bo.12.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1', 'subgroup_fusion': None, 'weyl_group': '8640.t'}
  • id: 246057126
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '216.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.r1', '72.l1', '108.p1'], 'contains': ['432.q1', '648.p1', '1080.ep1', '1296.u1', '2160.dz1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [479363884, 443555843884, 179159], 'label': '77760.bo.216.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.m1', 'old_label': '216.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.r1', 'subgroup_fusion': None, 'weyl_group': '240.189'}
  • id: 246056899
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.h1', '40.k1', '60.n1', '60.r1', '60.t1'], 'contains': ['240.v1', '240.ca1', '240.cb1', '360.bx1', '360.cl1', '1080.cv1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [193999357894, 280259481600, 482854444, 143975, 88695353644, 80787, 143304], 'label': '77760.bo.120.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '120.z1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.z1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 246056900
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.l1', '60.n1', '60.q1'], 'contains': ['240.v1', '240.cc1', '240.cd1', '360.by1', '360.cm1', '1080.cw1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [80787, 143304, 280259527104, 88695348625, 80880, 193999455627, 482808988], 'label': '77760.bo.120.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '120.ba1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.ba1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246056901
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1', '40.k1', '60.s1'], 'contains': ['240.w1', '240.ce1', '240.cf1', '360.bx1', '360.cn1', '1080.cz1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [193999277250, 280259481600, 482854444, 88695353644, 80787, 143304, 179159], 'label': '77760.bo.120.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.s1', 'old_label': '120.bb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bb1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246056902
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['30.i1', '40.h1', '60.o1'], 'contains': ['240.z1', '240.bd1', '240.be1', '240.bf1', '240.ck1', '360.bz1', '360.co1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [368871287518, 143975, 174436559403, 80880, 80787, 375138230375, 143304], 'label': '77760.bo.120.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '120.bc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bc1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246056903
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['30.j1', '40.h1', '60.o1'], 'contains': ['240.ba1', '240.bc1', '240.be1', '240.bj1', '240.ch1', '360.ca1', '360.co1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [143975, 80787, 519235320, 143304, 442641300482, 998144375, 80880], 'label': '77760.bo.120.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '120.bd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bd1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246056904
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.j1', '30.k1', '40.i1', '60.o1'], 'contains': ['240.z1', '240.ba1', '240.bb1', '240.bg1', '240.bn1', '240.bq1', '240.bu1', '360.cd1', '360.ce1', '360.cp1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [143975, 80787, 519235320, 143304, 442641386424, 998144375, 80880], 'label': '77760.bo.120.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '120.be1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.be1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246056905
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.k1', '30.l1', '40.j1', '60.o1'], 'contains': ['240.bb1', '240.bc1', '240.bd1', '240.bt1', '240.cn1', '360.ch1', '360.cq1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [368871287518, 143975, 375138270474, 174436559403, 80880, 80787, 143304], 'label': '77760.bo.120.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '120.bf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bf1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246056906
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.c1', '60.p1', '60.u1', '60.v1', '60.w1', '60.x1', '60.y1', '60.z1'], 'contains': ['240.bv1', '360.ci1', '360.cj1', '360.cw1', '480.g1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [442681119480, 355499200051, 355419504452, 143975, 80880, 80787, 143304], 'label': '77760.bo.120.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '120.bg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bg1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246056907
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.d1', '60.u1', '60.ba1', '60.bb1', '60.be1'], 'contains': ['240.bv1', '360.dj1', '360.dk1', '360.dl1', '360.dm1', '360.dn1', '480.h1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [461841004948, 462320323320, 143975, 19678982548, 262496684612, 80880, 80787], 'label': '77760.bo.120.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '120.bh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bh1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246056908
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.d1', '60.e1', '60.v1', '60.bc1', '60.bd1', '60.be1'], 'contains': ['240.bv1', '360.dh1', '360.do1', '360.dp1', '480.k1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [482711044, 143975, 188331136563, 87182201788, 80880, 80787, 375138230375], 'label': '77760.bo.120.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '120.bi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bi1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246056909
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': ['38880.c1', '38880.e1', '38880.a1', '38880.b1', '38880.g1', '38880.h1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.d1', '4.e1', '6.c1', '6.d1', '12.f1', '20.c1', '30.d1'], 'core': '2.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [183845, 143975, 93924236159, 80880, 80787, 462320328386], 'label': '77760.bo.2.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.d1', '4.e1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '77760.bo', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '77760.bo'}
  • id: 246056910
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.a1', '6.f1'], 'contains': ['24.b1', '24.d1', '24.e1', '36.c1', '36.g1', '60.e1', '72.c1', '120.j1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [174879491884, 183845, 143975, 462320328958, 80880, 80787], 'label': '77760.bo.12.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '12.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1', 'subgroup_fusion': None, 'weyl_group': '12960.bv'}
  • id: 246056911
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.m1', '60.b1', '60.f1', '60.q1'], 'contains': ['240.br1', '240.bw1', '240.cc1', '360.dq1', '360.dr1', '1080.dj1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [180587277504, 456053074316, 93448857748, 83543044, 174400173363, 80880, 80787], 'label': '77760.bo.120.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '120.bj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bj1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 246056912
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.m1', '60.a1', '60.g1', '60.q1'], 'contains': ['240.br1', '240.bx1', '240.cd1', '360.dr1', '360.ds1', '1080.dl1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [143975, 80787, 174400208787, 83548555, 93449036612, 180587232000, 456053212775], 'label': '77760.bo.120.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '120.bk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bk1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246056913
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.n1', '60.a1', '60.f1', '60.r1'], 'contains': ['240.br1', '240.by1', '240.cb1', '360.dt1', '360.du1', '1080.do1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [180587277504, 93448857748, 83543044, 174400173363, 456053150130, 80880, 80787], 'label': '77760.bo.120.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '120.bl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bl1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 246056914
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.n1', '60.s1'], 'contains': ['240.bs1', '240.bz1', '240.cf1', '360.dt1', '360.dv1', '1080.dp1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [174400208787, 93449001331, 456053150130, 83687012, 180587232000, 80787, 179159], 'label': '77760.bo.120.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.s1', 'old_label': '120.bm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bm1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246056915
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '40.o1', '60.b1', '60.g1', '60.r1'], 'contains': ['240.br1', '240.ca1', '360.dw1', '360.dx1', '1080.ec1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [180587277504, 93448857748, 83543044, 174400173363, 456053149444, 80880, 80787], 'label': '77760.bo.120.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '120.bn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bn1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 246056916
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1', '40.o1', '60.s1'], 'contains': ['240.bs1', '240.ce1', '360.dw1', '360.dy1', '1080.ed1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [174400208787, 93449001331, 83687012, 456053293412, 180587232000, 80787, 179159], 'label': '77760.bo.120.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.g1', 'old_label': '120.bo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bo1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246056955
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '160.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.d1', '80.g1', '80.k1', '80.s1'], 'contains': ['320.a1', '480.bg1', '480.bh1', '480.bi1', '480.bj1', '480.bk1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 10, 'diagramx': None, 'generators': [482808988, 143975, 193999455812, 280259527104, 80880, 80787], 'label': '77760.bo.160.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '160.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.h1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246056917
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.d1', '60.h1', '60.w1', '60.bc1', '60.bf1', '60.bh1', '60.bi1'], 'contains': ['240.bv1', '360.ev1', '360.ez1', '360.fa1', '360.fb1', '480.s1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [143975, 80787, 375138172555, 87661140722, 462320328958, 355462813680, 80880], 'label': '77760.bo.120.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '120.bp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bp1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246056918
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.e1', '60.e1', '60.i1', '60.x1', '60.ba1', '60.bg1', '60.bh1', '60.bi1'], 'contains': ['240.bv1', '360.ew1', '360.ex1', '360.ey1', '360.fc1', '480.v1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [143975, 80787, 443120250115, 442641300482, 80880, 442162067904, 180667065843], 'label': '77760.bo.120.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '120.bq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bq1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246056919
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.h1', '60.u1', '60.bd1', '60.bg1', '60.bj1'], 'contains': ['240.bv1', '360.fd1', '360.fe1', '360.fk1', '480.y1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [461841004948, 462320323891, 143975, 19678982548, 262496684612, 80880, 80787], 'label': '77760.bo.120.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '120.br1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.br1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246056920
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.f1', '60.i1', '60.v1', '60.bb1', '60.bf1', '60.bj1'], 'contains': ['240.bv1', '360.ff1', '360.fg1', '360.fh1', '360.fi1', '360.fj1', '480.bb1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [482711044, 375138087093, 143975, 188331136563, 87182201788, 80880, 80787], 'label': '77760.bo.120.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '120.bs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bs1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246056921
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.b1', '6.f1'], 'contains': ['24.b1', '24.e1', '24.f1', '36.d1', '36.h1', '60.i1', '72.d1', '120.l1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [174879492452, 183845, 143975, 80880, 80787, 462320328386], 'label': '77760.bo.12.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '12.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1', 'subgroup_fusion': None, 'weyl_group': '12960.bv'}
  • id: 246056922
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.j1', '60.l1', '60.y1', '60.ba1', '60.bc1', '60.bf1', '60.bg1'], 'contains': ['240.bv1', '360.fl1', '360.fm1', '360.fn1', '360.fo1', '480.be1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [143975, 80787, 87657511685, 87182201788, 374659447224, 19203926428, 80880], 'label': '77760.bo.120.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '120.bt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bt1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246056923
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.j1', '60.z1', '60.bb1', '60.bd1', '60.bh1'], 'contains': ['240.bv1', '360.fp1', '360.fq1', '360.fr1', '360.fs1', '360.ft1', '480.bi1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [262972240587, 355938186480, 87182202116, 143975, 374659447224, 80880, 80787], 'label': '77760.bo.120.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '120.bu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bu1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246056924
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.p1', '60.a1', '60.k1', '60.q1'], 'contains': ['240.bw1', '240.by1', '240.cd1', '360.fv1', '360.fx1', '1080.eu1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [180587277504, 93448857748, 83467916, 174400173363, 456053150130, 80880, 80787], 'label': '77760.bo.120.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '120.bv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bv1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246056925
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.m1', '40.q1', '60.b1', '60.k1', '60.t1'], 'contains': ['240.bw1', '240.ca1', '360.fw1', '360.ga1', '1080.fc1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [180587277504, 456053074316, 93448857748, 83467916, 174400173363, 80880, 80787], 'label': '77760.bo.120.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '120.bw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bw1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 246056926
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.p1', '60.c1', '60.f1', '60.q1'], 'contains': ['240.bx1', '240.by1', '240.cc1', '360.fx1', '360.fy1', '1080.fe1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [143975, 80787, 174400208787, 93449036612, 180587232000, 456053154955, 83543730], 'label': '77760.bo.120.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '120.bx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bx1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246056927
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.r1', '60.a1', '60.f1', '60.t1'], 'contains': ['240.bw1', '240.bx1', '240.cb1', '360.fz1', '360.gb1', '1080.fn1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [180587277504, 456053074316, 93448857748, 174400173363, 80880, 80787, 83467561], 'label': '77760.bo.120.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '120.by1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.by1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246056928
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.c1', '40.q1', '60.c1', '60.g1', '60.t1'], 'contains': ['240.bx1', '240.ca1', '360.ga1', '360.gc1', '1080.fo1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [143975, 80787, 174400208787, 83548555, 93449036612, 180587232000, 456053154955], 'label': '77760.bo.120.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '120.bz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bz1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246056929
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.n1', '40.s1', '60.c1', '60.k1', '60.r1'], 'contains': ['240.by1', '240.ca1', '360.gd1', '360.ge1', '1080.fz1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [174400208787, 93449036612, 83543730, 143975, 456053150130, 180587232000, 80787], 'label': '77760.bo.120.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '120.ca1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.ca1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 246056930
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1', '40.s1', '60.s1'], 'contains': ['240.bz1', '240.ce1', '360.gd1', '360.gf1', '1080.ga1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [174400208787, 93449001331, 83543730, 456053150130, 180587232000, 80787, 179159], 'label': '77760.bo.120.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.s1', 'old_label': '120.cb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.cb1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246056931
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '120.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '60.l1', '60.z1', '60.be1', '60.bi1', '60.bj1'], 'contains': ['240.bv1', '360.fu1', '360.gg1', '360.gh1', '480.n1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [143975, 87182201788, 19203926428, 374659447224, 80880, 80787, 87657338304], 'label': '77760.bo.120.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '120.cc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.cc1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246056932
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.c1', '6.f1'], 'contains': ['24.b1', '24.c1', '36.i1', '60.p1', '72.f1', '120.u1'], 'core': '720.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [143975, 349232267045, 455574148294, 85805, 80880, 80787, 143304], 'label': '77760.bo.12.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '12.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1', 'subgroup_fusion': None, 'weyl_group': '12960.bv'}
  • id: 246056933
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '135.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['9.a1', '45.a1'], 'contains': ['270.a1', '270.b1', '270.c1', '270.d1', '270.i1', '270.m1', '270.q1', '270.s1', '270.u1', '270.v1', '270.w1', '270.bt1', '270.bv1', '270.by1', '270.cb1', '405.a1', '405.b1', '540.br1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [262496868215, 362615, 461841090505, 45363, 5066, 448908283914, 19679027763, 462320011466], 'label': '77760.bo.135.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '135.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '135.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246056934
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '135.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.b1', '45.a1'], 'contains': ['270.k1', '270.n1', '270.p1', '270.t1', '270.x1', '270.y1', '270.z1', '270.bl1', '270.bm1', '270.bn1', '270.bo1', '405.a1', '405.c1', '540.bt1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [482849425, 87661059842, 355462916645, 85805, 375138172205, 80787, 462320046985, 143304], 'label': '77760.bo.135.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '135.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '135.b1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246056935
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '135.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['45.a1', '45.b1'], 'contains': ['270.f1', '270.g1', '270.h1', '270.j1', '270.o1', '270.r1', '270.ba1', '270.bb1', '270.bc1', '270.bd1', '270.be1', '270.bf1', '270.bg1', '270.bh1', '270.bi1', '270.bj1', '270.bk1', '270.bp1', '270.bq1', '270.br1', '270.bs1', '270.bw1', '270.ca1', '405.b1', '405.c1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [461841090505, 143975, 178680, 80787, 462320328485, 448908284158, 19679028004, 5309], 'label': '77760.bo.135.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '135.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '135.c1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246056936
    {'ambient': '77760.bo', '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': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.b1', '72.c1', '72.d1', '72.f1'], 'contains': ['288.a1', '288.c1', '288.d1', '432.a1', '432.c1', '720.bc1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1037836800, 143975, 85805, 80880, 80787, 18764565242], 'label': '77760.bo.144.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '144.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.a1', 'subgroup_fusion': None, 'weyl_group': '2160.cr'}
  • id: 246056937
    {'ambient': '77760.bo', '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': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.f1'], 'contains': ['288.a1', '288.d1', '288.e1', '432.b1', '432.d1', '720.bk1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [18764743922, 183845, 1037980104, 143975, 80880, 80787], 'label': '77760.bo.144.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '144.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b1', 'subgroup_fusion': None, 'weyl_group': '2160.cr'}
  • id: 246056938
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1'], 'contains': ['288.a1', '288.b1', '432.e1', '720.a1'], 'core': '720.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18764743922, 143975, 85805, 80880, 80787, 143304], 'label': '77760.bo.144.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '144.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1', 'subgroup_fusion': None, 'weyl_group': '432.300'}
  • id: 246056939
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '72.f1', '72.i1', '72.j1'], 'contains': ['288.b1', '288.c1', '288.e1', '432.f1', '432.g1', '720.ck1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1037980104, 18764748747, 143975, 80880, 80787, 143304], 'label': '77760.bo.144.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '144.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 246056940
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '144.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1'], 'contains': ['288.b1', '288.d1', '432.h1', '720.cm1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18764748747, 143975, 1038020645, 80880, 80787, 143304], 'label': '77760.bo.144.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '144.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.e1', 'subgroup_fusion': None, 'weyl_group': '2160.cr'}
  • id: 246056941
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '144.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1', '72.c1', '72.i1'], 'contains': ['288.c1', '432.i1', '432.m1', '720.dv1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [181146211175, 269202707012, 143975, 267842045067, 80880, 80787], 'label': '77760.bo.144.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '144.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.f1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 246056942
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '144.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.e1', '72.c1', '72.d1', '72.j1'], 'contains': ['288.c1', '432.j1', '432.k1', '720.dz1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [269202707012, 143975, 267842045067, 80880, 80787, 181146153355], 'label': '77760.bo.144.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '144.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.g1', 'subgroup_fusion': None, 'weyl_group': '2160.cr'}
  • id: 246056943
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '6.e1', '6.g1', '6.i1'], 'contains': ['24.a1', '36.k1', '36.o1', '72.g1', '120.z1', '180.cn1'], 'core': '24.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [274511462400, 87182202116, 143975, 80787, 143304], 'label': '77760.bo.12.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1', 'subgroup_fusion': None, 'weyl_group': '8640.t'}
  • id: 246056944
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '144.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1', '72.d1', '72.i1'], 'contains': ['288.c1', '432.l1', '432.n1', '720.ea1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [181146067893, 269202707012, 143975, 267842045067, 80880, 80787], 'label': '77760.bo.144.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '144.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.h1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 246056945
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '144.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.a1', '48.a1', '72.b1', '72.e1', '72.g1', '72.k1', '72.m1', '72.n1', '72.o1'], 'contains': ['432.o1', '432.p1', '720.ef1', '864.e1', '1440.bf1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [349232083200, 455574147987, 80880, 80787], 'label': '77760.bo.144.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '144.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.i1', 'subgroup_fusion': None, 'weyl_group': '1440.5849'}
  • id: 246056946
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '144.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.g1', '48.a1', '72.h1', '72.l1', '72.p1'], 'contains': ['432.o1', '432.q1', '720.ei1', '864.f1', '1440.bg1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [455574210931, 349232083200, 80787, 179159], 'label': '77760.bo.144.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '144.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.j1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 246056947
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '160.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.a1', '80.b1', '80.c1', '80.d1', '80.e1'], 'contains': ['320.a1', '480.a1', '480.b1', '480.c1', '480.d1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [183845, 143975, 280259700485, 193999455812, 80880, 80787], 'label': '77760.bo.160.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '160.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.a1', 'subgroup_fusion': None, 'weyl_group': '864.2470'}
  • id: 246056948
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '160.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.e1', '80.f1', '80.g1', '80.h1', '80.i1'], 'contains': ['320.a1', '480.e1', '480.f1', '480.g1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 10, 'diagramx': None, 'generators': [193999357894, 143975, 280259527104, 80880, 80787, 143304], 'label': '77760.bo.160.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '160.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.b1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 246056949
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '160.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.a1', '80.f1', '80.j1', '80.k1', '80.l1'], 'contains': ['320.a1', '480.h1', '480.i1', '480.j1', '480.k1', '480.l1', '480.m1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [93449001331, 143975, 83641651, 174400173363, 80880, 80787], 'label': '77760.bo.160.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '160.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.c1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 246056950
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '160.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.b1', '80.g1', '80.l1', '80.m1', '80.n1', '80.o1', '80.p1', '80.q1'], 'contains': ['320.a1', '480.n1', '480.o1', '480.p1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 10, 'diagramx': None, 'generators': [482711044, 143975, 193999455812, 280259527104, 80880, 80787], 'label': '77760.bo.160.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '160.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.d1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246056951
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '160.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['80.a1', '80.c1', '80.h1', '80.j1', '80.m1', '80.r1', '80.s1'], 'contains': ['320.a1', '480.q1', '480.r1', '480.s1', '480.t1', '480.u1', '480.v1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 80, 'diagramx': None, 'generators': [456053074316, 93449001331, 143975, 174400173363, 80880, 80787], 'label': '77760.bo.160.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '160.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.e1', 'subgroup_fusion': None, 'weyl_group': '1296.2985'}
  • id: 246056952
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '160.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.c1', '80.f1', '80.k1', '80.n1', '80.r1'], 'contains': ['320.a1', '480.w1', '480.x1', '480.y1', '480.z1', '480.ba1', '480.bb1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [93449001331, 143975, 174400173363, 456053150130, 80880, 80787], 'label': '77760.bo.160.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '160.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.f1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 246056953
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '160.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.b1', '80.d1', '80.i1', '80.j1', '80.r1'], 'contains': ['320.a1', '480.bc1', '480.bd1', '480.be1', '480.bf1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [143975, 193999455812, 280259527104, 482768881, 80880, 80787], 'label': '77760.bo.160.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '160.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.g1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246056954
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '6.h1'], 'contains': ['24.g1', '36.k1', '36.p1', '72.h1', '120.bb1', '180.co1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [274511462400, 178680, 87182202116, 80787, 179159], 'label': '77760.bo.12.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '12.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
  • id: 246056957
    {'ambient': '77760.bo', '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': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.a1', '90.e1'], 'contains': ['360.b1', '360.c1', '360.e1', '360.ds1', '360.du1', '360.fv1', '360.fz1', '540.c1', '1620.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [174400128000, 143975, 180587232000, 456053154955, 85805, 93449001575, 83606375], 'label': '77760.bo.180.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '180.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.a1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246056958
    {'ambient': '77760.bo', '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': '12960.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.a1', '60.b1', '90.e1'], 'contains': ['360.b1', '360.d1', '360.dq1', '360.dx1', '360.fw1', '540.d1', '1620.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [93449082115, 456053207518, 174400128000, 224515, 85946, 180587232000, 83686915], 'label': '77760.bo.180.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '180.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.b1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246056959
    {'ambient': '77760.bo', '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': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.b1', '60.c1', '90.e1'], 'contains': ['360.c1', '360.d1', '360.fy1', '360.gc1', '360.ge1', '540.h1', '1620.o1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [180587232243, 93448857748, 83462998, 456053073961, 148, 174400128148, 5759], 'label': '77760.bo.180.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '180.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.c1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246056960
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.d1', '90.a1', '90.c1', '90.r1'], 'contains': ['360.o1', '360.dj1', '360.ev1', '540.a1', '540.s1', '540.t1', '540.u1', '720.f1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 80787, 87660962042, 462320328485, 375138305757, 355462738109, 5309], 'label': '77760.bo.180.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.d1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246056961
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.c1', '60.e1', '90.b1', '90.c1', '90.s1'], 'contains': ['360.o1', '360.do1', '360.ew1', '540.b1', '540.q1', '540.w1', '720.g1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [443120071204, 183845, 442641024148, 180667249346, 442162067904, 80880, 80787], 'label': '77760.bo.180.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.e1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246056962
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.f1', '90.e1'], 'contains': ['360.m1', '360.p1', '360.u1', '360.dq1', '360.du1', '360.fy1', '360.fz1', '540.c1', '1620.bi1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [180587232243, 93448857748, 83462998, 456053073961, 5066, 148, 174400128148], 'label': '77760.bo.180.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '180.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.f1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246056963
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.a1', '60.f1', '90.f1'], 'contains': ['360.l1', '360.q1', '360.s1', '360.dr1', '360.dt1', '360.fx1', '360.gb1', '540.c1', '1620.bk1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [40349, 174400208787, 83543730, 93448938387, 456053073961, 180587232000, 80787], 'label': '77760.bo.180.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '180.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.g1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246056964
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.c1', '60.b1', '60.g1', '90.f1'], 'contains': ['360.l1', '360.r1', '360.dr1', '360.dw1', '360.ga1', '540.d1', '1620.bo1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [80787, 174400208787, 83462400, 93448938387, 180587232000, 86155, 456053154955], 'label': '77760.bo.180.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '180.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.h1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246056965
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.d1', '6.f1'], 'contains': ['24.c1', '24.d1', '24.f1', '36.l1', '36.m1', '60.v1', '72.i1', '120.be1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [479363884, 143975, 443555763716, 80880, 80787, 143304], 'label': '77760.bo.12.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '12.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1', 'subgroup_fusion': None, 'weyl_group': '4320.bp'}
  • id: 246056966
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.d1', '60.g1', '90.e1'], 'contains': ['360.m1', '360.t1', '360.ds1', '360.dx1', '360.gc1', '540.d1', '1620.bp1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [180587277504, 83507904, 174400208880, 40585, 456053073961, 93448938480, 80880], 'label': '77760.bo.180.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '180.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.i1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246056967
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.h1', '90.b1', '90.d1', '90.r1'], 'contains': ['360.o1', '360.ez1', '360.fd1', '540.e1', '540.bf1', '540.bj1', '720.o1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [355462738109, 87661059842, 5309, 143975, 462320328958, 375138172555, 80787], 'label': '77760.bo.180.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.j1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246056968
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.d1', '60.i1', '90.a1', '90.d1', '90.s1'], 'contains': ['360.o1', '360.fc1', '360.ff1', '540.f1', '540.bg1', '540.bh1', '540.bi1', '720.r1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [87182277597, 277050, 482988094, 188331136563, 375138172205, 80880, 80787], 'label': '77760.bo.180.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.k1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246056969
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.j1', '90.a1', '90.b1', '90.t1'], 'contains': ['360.o1', '360.fo1', '360.fp1', '540.g1', '540.bl1', '540.bm1', '540.bn1', '720.t1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [374659361758, 355938463434, 87181925066, 277050, 262972155450, 80880, 80787], 'label': '77760.bo.180.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.l1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246056970
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.e1', '60.k1', '90.e1'], 'contains': ['360.p1', '360.t1', '360.fv1', '360.fw1', '360.ge1', '540.h1', '1620.bv1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [93448857748, 174400128148, 83462998, 180587232243, 5066, 456053074316, 148], 'label': '77760.bo.180.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '180.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.m1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246056971
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.f1', '60.c1', '60.k1', '90.f1'], 'contains': ['360.q1', '360.r1', '360.fx1', '360.ga1', '360.gd1', '540.h1', '1620.bz1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [40349, 174400208787, 83543730, 93448938387, 456053154955, 180587232000, 80787], 'label': '77760.bo.180.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '180.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.n1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246056972
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.d1', '60.l1', '90.c1', '90.d1', '90.t1'], 'contains': ['360.o1', '360.fl1', '360.gg1', '540.i1', '540.bo1', '540.bp1', '720.k1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [374659361758, 355938463434, 87182277597, 277050, 262972155450, 80880, 80787], 'label': '77760.bo.180.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.o1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246056973
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.m1', '90.e1'], 'contains': ['360.a1', '360.b1', '360.c1', '360.g1', '360.m1', '360.p1', '360.v1', '360.w1', '360.cc1', '360.cf1', '360.ck1', '540.j1', '540.br1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [174400128000, 143975, 143304, 180587232000, 456053154955, 85805, 93449001575], 'label': '77760.bo.180.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '180.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.p1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246056974
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.g1', '60.n1', '90.e1'], 'contains': ['360.d1', '360.e1', '360.t1', '360.u1', '360.w1', '360.cl1', '360.cm1', '540.k1', '1620.cm1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [482849425, 143975, 193999277493, 40585, 280259522185, 88695348625, 143304], 'label': '77760.bo.180.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '180.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.q1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057127
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '216.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.s1', '72.m1', '108.b1', '108.g1', '108.q1'], 'contains': ['432.p1', '648.q1', '1080.gk1', '1296.r1', '2160.ev1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [143975, 462320328386, 174879451586], 'label': '77760.bo.216.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.s1', 'subgroup_fusion': None, 'weyl_group': '240.189'}
  • id: 246056975
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.m1', '90.f1'], 'contains': ['360.j1', '360.l1', '360.q1', '360.x1', '360.y1', '360.bu1', '360.bv1', '360.bw1', '540.j1', '540.bt1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [80787, 174400208787, 93448938387, 180587232000, 45813, 83543730, 40349], 'label': '77760.bo.180.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '180.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.r1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246056976
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.e1', '6.f1'], 'contains': ['24.c1', '24.e1', '36.n1', '60.x1', '72.j1', '120.bf1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [479278229, 443555839197, 143975, 80880, 80787, 143304], 'label': '77760.bo.12.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '12.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1', 'subgroup_fusion': None, 'weyl_group': '12960.bv'}
  • id: 246056977
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1', '60.n1', '90.f1'], 'contains': ['360.r1', '360.s1', '360.y1', '360.bx1', '360.by1', '540.k1', '1620.cq1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [482849425, 280259567405, 193999455627, 85805, 80787, 88695348625, 143304], 'label': '77760.bo.180.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '180.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.s1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246056978
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.g1', '90.n1', '90.u1'], 'contains': ['360.bc2', '360.bg1', '360.bh1', '360.de1', '360.dg1', '360.ee1', '360.ef1', '540.l1', '540.bv1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [7185029309, 143975, 19678982548, 85805, 80880, 80787, 462320328386], 'label': '77760.bo.180.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.t1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.t1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246056979
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.l1', '90.u1'], 'contains': ['360.bc2', '360.bi1', '360.bj1', '360.df1', '360.dg1', '360.eg1', '360.eh1', '540.m1', '540.bw1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [7185162389, 143975, 19678982548, 85805, 80880, 80787, 462320328386], 'label': '77760.bo.180.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.u1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.u1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246056980
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.i1', '90.l1', '90.v1'], 'contains': ['360.bc1', '360.bj1', '360.bk1', '360.dc1', '360.dd1', '360.ec1', '360.ed1', '540.n1', '540.bx1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [87182277125, 143975, 375138270474, 482768881, 85805, 80880, 80787], 'label': '77760.bo.180.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.v1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.v1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246056981
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['20.a1', '90.h1', '90.l1', '90.w1'], 'contains': ['360.bc1', '360.bf1', '360.bi1', '360.cz1', '360.db1', '360.ea1', '360.ek1', '540.o1', '540.by1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [456053207518, 87262035243, 83543730, 143975, 85805, 80880, 80787], 'label': '77760.bo.180.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.w1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.w1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246056982
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.g1', '90.l1', '90.x1'], 'contains': ['360.bb1', '360.bb2', '360.bc2', '360.bf1', '360.bk1', '360.cx1', '360.cx2', '360.cy1', '360.da1', '360.dz1', '360.ei1', '540.p1', '540.bz1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 19678982548, 461841188401, 85805, 80880, 80787, 462320328386], 'label': '77760.bo.180.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.x1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.x1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246056983
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.x2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.h1', '90.i1', '90.x1'], 'contains': ['360.bb1', '360.bb2', '360.bc1', '360.bf2', '360.bk1', '360.cx1', '360.cx3', '360.cy2', '360.da2', '360.dz2', '360.ei1', '540.p2', '540.bz2'], 'core': '1440.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 80787, 461841188401, 85805, 462320328958, 19678982548, 80880], 'label': '77760.bo.180.x2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.x2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.x2', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246056984
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.e1', '90.h1', '90.n1', '90.v1'], 'contains': ['360.bc1', '360.bg1', '360.bo1', '360.dc1', '360.dh1', '360.eb1', '360.ey1', '540.q1', '540.ca1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 80787, 442641386424, 443120250115, 183845, 80880, 180667249346], 'label': '77760.bo.180.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.y1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.y1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246056985
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['20.b1', '90.i1', '90.n1', '90.w1'], 'contains': ['360.bc1', '360.bh1', '360.cz1', '360.di1', '360.ej1', '540.r1', '540.cb1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [456053207518, 87262035243, 143975, 83641651, 85805, 80880, 80787], 'label': '77760.bo.180.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.z1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.z1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246056986
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.d1', '90.j1', '90.o1', '90.r1'], 'contains': ['360.bm1', '360.dj1', '360.ez1', '540.t1', '540.v1', '540.cc1', '720.y1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [355462738109, 87660962042, 85805, 375138172205, 80880, 80787, 462320046985], 'label': '77760.bo.180.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '180.ba1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.ba1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246056987
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '6.h1'], 'contains': ['24.g1', '36.a1', '36.r1', '72.l1', '120.bo1', '180.ef1'], 'core': '36.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [93924374131, 462320323467, 80787, 179159], 'label': '77760.bo.12.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '12.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
  • id: 246056988
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.d1', '90.k1'], 'contains': ['360.bn1', '360.dk1', '360.fa1', '540.u1', '540.cc1', '720.z1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [461841090505, 19678982548, 85805, 262496684612, 80880, 80787, 462320046985], 'label': '77760.bo.180.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1', 'old_label': '180.bb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bb1', 'subgroup_fusion': None, 'weyl_group': '1296.2931'}
  • id: 246056989
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.d1', '90.l1', '90.n1', '90.x1'], 'contains': ['360.bc1', '360.bc2', '360.bo1', '360.cy1', '360.cy2', '360.dl1', '360.fb1', '540.s1', '540.cc1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [183845, 143975, 19678982548, 461841188401, 462320328958, 80880, 80787], 'label': '77760.bo.180.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '180.bc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bc1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246056990
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.g1', '60.e1', '90.m1', '90.o1', '90.s1'], 'contains': ['360.bm1', '360.do1', '360.fc1', '540.w1', '540.x1', '540.ca1', '720.bb1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [183845, 87182277597, 188331171987, 482849425, 143975, 375138172555, 80787], 'label': '77760.bo.180.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '180.bd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bd1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246056991
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.h1', '90.u1'], 'contains': ['360.bf2', '360.bg1', '360.bi1', '360.ee1', '360.eg1', '360.en1', '360.ep1', '540.y1', '540.cd1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [7185029309, 143975, 19678982548, 462320328958, 85805, 80880, 80787], 'label': '77760.bo.180.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.be1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.be1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246056992
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.i1', '90.p1', '90.u1'], 'contains': ['360.bf2', '360.bh1', '360.bj1', '360.ef1', '360.eh1', '360.eo1', '360.ep1', '540.z1', '540.ce1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [183845, 7185029309, 143975, 19678982548, 80880, 80787, 462320328386], 'label': '77760.bo.180.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.bf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bf1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246056993
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.g1', '90.h1', '90.v1'], 'contains': ['360.bf1', '360.bg1', '360.bk1', '360.eb1', '360.ed1', '360.el1', '360.em1', '540.ba1', '540.cf1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 80787, 180667151546, 442641386755, 443120250115, 183845, 80880], 'label': '77760.bo.180.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.bg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bg1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246056994
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['20.c1', '90.g1', '90.p1', '90.w1'], 'contains': ['360.bf1', '360.bh1', '360.ea1', '360.ej1', '360.eq1', '540.bb1', '540.cg1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [456053074316, 87262035243, 83543730, 143975, 85805, 80880, 80787], 'label': '77760.bo.180.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.bh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bh1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246056995
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.g1', '90.i1', '90.y1'], 'contains': ['360.bh1', '360.bk1', '360.er1', '360.es1', '360.eu1', '540.bc1', '540.ch1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [374659361758, 183845, 87182277125, 143975, 355938110909, 80880, 80787], 'label': '77760.bo.180.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.bi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bi1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246056996
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.h1', '90.m1', '90.q1', '90.r1'], 'contains': ['360.bm1', '360.ev1', '360.fd1', '540.bd1', '540.bf1', '540.cj1', '720.be1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [80787, 87661244013, 85805, 375138363450, 462320328958, 355462738109, 80880], 'label': '77760.bo.180.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.bj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bj1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246056997
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.h1', '60.i1', '90.j1', '90.q1', '90.s1'], 'contains': ['360.bm1', '360.ew1', '360.ff1', '540.be1', '540.bh1', '540.ci1', '720.bf1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [183845, 87182277597, 188331171987, 482849425, 143975, 375138270474, 80787], 'label': '77760.bo.180.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.bk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bk1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246056998
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.d1', '6.b1', '6.d1', '6.i1'], 'contains': ['24.a1', '36.s1', '36.t1', '72.m1', '120.bw1', '180.ey1'], 'core': '24.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [143975, 93924409412, 80787, 462320328386], 'label': '77760.bo.12.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1', 'subgroup_fusion': None, 'weyl_group': '8640.t'}
  • id: 246056999
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.i1', '90.k1'], 'contains': ['360.bn1', '360.ex1', '360.fg1', '540.bi1', '540.ci1', '720.bg1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [80787, 375138172555, 188331315812, 87181925066, 85805, 482635561, 80880], 'label': '77760.bo.180.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.k1', 'old_label': '180.bl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bl1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
  • id: 246057000
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.i1', '90.l1', '90.p1', '90.v1'], 'contains': ['360.bf1', '360.bj1', '360.bo1', '360.ec1', '360.el1', '360.ey1', '360.fh1', '540.bg1', '540.ci1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 80787, 87182277125, 375138172555, 85805, 482635561, 80880], 'label': '77760.bo.180.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.bm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bm1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057001
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.h1', '90.h1', '90.p1', '90.x1'], 'contains': ['360.bf1', '360.bf2', '360.bo1', '360.dz1', '360.dz2', '360.fb1', '360.fk1', '540.bj1', '540.cj1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [183845, 448908283441, 143975, 19678982548, 80880, 80787, 462320328386], 'label': '77760.bo.180.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '180.bn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bn1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057002
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.j1', '90.j1', '90.m1', '90.t1'], 'contains': ['360.bm1', '360.fl1', '360.fp1', '540.bk1', '540.bm1', '540.ck1', '720.bi1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [87182277597, 374659170505, 355938110909, 85805, 80880, 80787, 262971964205], 'label': '77760.bo.180.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.bo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bo1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246057003
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.j1', '90.k1'], 'contains': ['360.bn1', '360.fm1', '360.fq1', '540.bn1', '540.ck1', '720.bj1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [183845, 87182277597, 143975, 374659361850, 19203926428, 87657516984, 80787], 'label': '77760.bo.180.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.k1', 'old_label': '180.bp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bp1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
  • id: 246057004
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.j1', '90.h1', '90.l1', '90.y1'], 'contains': ['360.bi1', '360.bk1', '360.bo1', '360.er1', '360.et1', '360.fn1', '360.fr1', '540.bl1', '540.ck1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 80787, 374659361758, 87182277125, 355938243989, 183845, 80880], 'label': '77760.bo.180.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.bq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bq1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057005
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.l1', '90.n1', '90.p1', '90.y1'], 'contains': ['360.bh1', '360.bo1', '360.es1', '360.fn1', '360.fu1', '540.bo1', '540.cl1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [374659361282, 87182277125, 143975, 355938110909, 85805, 80880, 80787], 'label': '77760.bo.180.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.br1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.br1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057006
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.a1', '60.l1', '90.o1', '90.q1', '90.t1'], 'contains': ['360.bm1', '360.fo1', '360.gg1', '540.bp1', '540.bq1', '540.cl1', '720.bd1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [374659170505, 87181925066, 19203654963, 85805, 80880, 80787, 87657338304], 'label': '77760.bo.180.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '180.bs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bs1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246057007
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.i1', '45.a1', '60.m1', '60.o1'], 'contains': ['360.f1', '360.h1', '360.k1', '360.n1', '360.z1', '360.bd1', '360.be1', '360.bl1', '360.bp1', '360.bq1', '360.br1', '360.bz1', '360.ca1', '360.cd1', '360.ch1', '540.br1', '540.bt1', '540.cm1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [442641386187, 998099012, 143975, 519235320, 85805, 80787, 143304], 'label': '77760.bo.180.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '180.bt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bt1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057008
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.i1', '60.p1', '90.r1', '90.s1', '90.t1'], 'contains': ['360.o1', '360.bm1', '360.ci1', '540.bs1', '540.bu1', '540.cp1', '720.bl1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [274467962404, 143975, 194518339175, 268244605587, 85805, 80787, 143304], 'label': '77760.bo.180.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.bu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bu1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246057009
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.e1', '6.c1', '6.d1', '6.g1'], 'contains': ['24.a1', '36.v1', '36.w1', '72.o1', '120.ca1', '180.fa1'], 'core': '24.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [93924311187, 462320323891, 80880, 80787], 'label': '77760.bo.12.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1', 'subgroup_fusion': None, 'weyl_group': '8640.t'}
  • id: 246057010
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.o1', '90.v1', '90.w1', '90.x1'], 'contains': ['360.bb1', '360.bc1', '360.bf1', '360.bs1', '360.bt1', '360.co1', '360.cp1', '360.cq1', '540.cm1'], 'core': '720.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [143975, 80787, 143304, 85805, 442641386424, 443120250115, 80880], 'label': '77760.bo.180.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.bv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bv1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057011
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.bv2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.u1', '90.x1'], 'contains': ['360.bb2', '360.bc2', '360.bf2', '360.bs1', '360.bt1', '360.co2', '360.cp2', '360.cq2', '540.cm2'], 'core': '720.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [143975, 80787, 143304, 85805, 442641386424, 448908283914, 80880], 'label': '77760.bo.180.bv2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.bv2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bv2', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246057012
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1', '90.u1', '90.v1'], 'contains': ['360.bg1', '360.bj1', '360.bt1', '360.cs1', '360.cv1', '540.cn1'], 'core': '720.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [267845679213, 443120250115, 143975, 85805, 80880, 80787, 143304], 'label': '77760.bo.180.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.bw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bw1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057013
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.e1', '90.u1', '90.w1', '90.y1'], 'contains': ['360.bh1', '360.bi1', '360.bt1', '360.ct1', '360.cu1', '540.co1'], 'core': '720.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [143975, 80787, 482768881, 143304, 88695348625, 85805, 80880], 'label': '77760.bo.180.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.bx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bx1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057014
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.p1', '90.v1', '90.x1', '90.y1'], 'contains': ['360.bk1', '360.bo1', '360.bt1', '360.cr1', '360.cw1', '540.cp1'], 'core': '720.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [355499159518, 143975, 442681079189, 85805, 80880, 80787, 143304], 'label': '77760.bo.180.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '180.by1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.by1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057015
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.q1', '90.f1'], 'contains': ['360.bv1', '360.bw1', '360.by1', '360.dr1', '360.fx1', '540.cs1', '1620.ct1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [80787, 174400208787, 93448938387, 83548555, 180587232000, 45813, 456053150130], 'label': '77760.bo.180.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '180.bz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bz1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057016
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.j1', '60.r1', '60.s1', '90.f1'], 'contains': ['360.bv1', '360.bx1', '360.dt1', '360.dw1', '360.gd1', '540.ct1', '1620.cy1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [80787, 174400208787, 93448938387, 180587232000, 45813, 83543730, 456053150130], 'label': '77760.bo.180.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '180.ca1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.ca1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246057017
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.k1', '60.t1', '90.f1'], 'contains': ['360.bw1', '360.bx1', '360.ga1', '360.gb1', '540.cx1', '1620.dg1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [83548555, 174400208787, 93448938387, 456053154955, 180587232000, 80787, 693], 'label': '77760.bo.180.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '180.cb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.cb1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057018
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.u1', '90.r1', '90.z1', '90.bb1'], 'contains': ['360.ci1', '360.dj1', '360.fd1', '540.cq1', '540.dj1', '540.dl1', '540.dm1', '720.bq1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [462320323320, 19679028004, 143975, 461841050404, 80787, 262496586694, 143304], 'label': '77760.bo.180.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.cc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.cc1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246057019
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.u1', '90.bc1'], 'contains': ['360.cj1', '360.dm1', '360.fe1', '540.cq1', '540.dk1', '540.dn1', '540.do1', '720.br1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [178680, 355462911480, 462320323467, 375138311012, 87661145547, 80787, 179159], 'label': '77760.bo.180.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '180.cd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.cd1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057020
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': ['38880.c1', '38880.e1', '38880.f1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '6.e1', '12.g1', '20.e1', '30.h1'], 'core': '2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [87182277597, 143975, 85805, 274511507904, 80880, 80787, 143304], 'label': '77760.bo.2.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '720.a1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '77760.bo', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '77760.bo'}
  • id: 246057021
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '6.h1'], 'contains': ['24.g1', '36.v1', '36.x1', '72.p1', '120.cb1', '180.fb1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [93924374131, 462320323891, 80787, 179159], 'label': '77760.bo.12.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '12.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
  • id: 246057022
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.l1', '60.v1', '90.s1', '90.ba1', '90.bb1'], 'contains': ['360.ci1', '360.do1', '360.ff1', '540.cr1', '540.df1', '540.dp1', '720.bs1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [442641386187, 180667209003, 224184, 443120250115, 143975, 442162022400, 80787], 'label': '77760.bo.180.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.ce1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.ce1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246057023
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.m1', '60.v1', '90.bc1'], 'contains': ['360.cj1', '360.dp1', '360.fi1', '540.cr1', '540.dg1', '540.dq1', '720.bt1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [188331315147, 178680, 375138311012, 87182202116, 482773948, 80787, 179159], 'label': '77760.bo.180.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '180.cf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.cf1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057024
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.q1', '90.e1'], 'contains': ['360.cf1', '360.ck1', '360.cm1', '360.dq1', '360.ds1', '360.fv1', '360.fy1', '540.cs1', '1620.dt1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [93449082115, 83548555, 224184, 456053069398, 174400128000, 224515, 180587232000], 'label': '77760.bo.180.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '180.cg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.cg1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057025
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.l1', '60.r1', '90.e1'], 'contains': ['360.cf1', '360.cl1', '360.du1', '360.dx1', '360.ge1', '540.ct1', '1620.ea1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [93449082115, 224184, 456053069398, 83462998, 174400128000, 224515, 180587232000], 'label': '77760.bo.180.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '180.ch1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.ch1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057026
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1', '60.s1'], 'contains': ['360.cg1', '360.cn1', '360.dv1', '360.dy1', '360.gf1', '540.ct1', '1620.eb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [178680, 456053069398, 83462998, 174400128000, 93449036759, 180587232000, 179159], 'label': '77760.bo.180.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.s1', 'old_label': '180.ci1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.ci1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057027
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.w1', '90.r1', '90.ba1', '90.bd1'], 'contains': ['360.ci1', '360.ev1', '360.ez1', '540.cu1', '540.dw1', '540.ea1', '720.cc1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [178680, 355462911480, 87661059842, 143975, 462320328485, 80787, 375138305757], 'label': '77760.bo.180.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.cj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.cj1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246057028
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.n1', '60.x1', '90.s1', '90.z1', '90.bd1'], 'contains': ['360.ci1', '360.ew1', '360.fc1', '540.cv1', '540.dx1', '540.dy1', '540.dz1', '720.cf1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [180667289547, 178680, 442641300482, 443120250115, 143975, 442162022400, 80787], 'label': '77760.bo.180.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.ck1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.ck1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246057029
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.y1', '90.t1', '90.z1', '90.ba1'], 'contains': ['360.ci1', '360.fl1', '360.fo1', '540.cw1', '540.eb1', '540.ec1', '540.ed1', '720.cg1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [87182277597, 362615, 355938186480, 374659447555, 262972241015, 80880, 80787], 'label': '77760.bo.180.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.cl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.cl1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246057030
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.n1', '60.t1', '90.e1'], 'contains': ['360.ck1', '360.cl1', '360.fw1', '360.fz1', '360.gc1', '540.cx1', '1620.eh1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [174400128000, 143975, 143304, 83548555, 180587232000, 456053154955, 93449001575], 'label': '77760.bo.180.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '180.cm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.cm1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057031
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.h1', '60.z1', '90.t1', '90.bb1', '90.bd1'], 'contains': ['360.ci1', '360.fp1', '360.gg1', '540.cy1', '540.ee1', '540.eg1', '720.by1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [224184, 19203926999, 143975, 374659447652, 87657516984, 80787, 87182201971], 'label': '77760.bo.180.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.cn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.cn1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246057032
    {'ambient': '77760.bo', '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': '38880.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['30.a1', '30.b1', '30.c1', '30.d1', '30.f1', '30.g1', '30.h1', '30.i1', '30.j1', '30.k1', '30.l1', '45.a1', '45.b1', '60.o1'], 'core': '720.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [461841090505, 143975, 80787, 262496586694, 143304, 85805, 19678982548, 448908283914, 80880, 462320328386], 'label': '77760.bo.15.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '15.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.a1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246057033
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.i1', '60.z1', '90.bc1'], 'contains': ['360.cj1', '360.fs1', '360.gh1', '540.cy1', '540.ef1', '540.eh1', '720.bz1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [224184, 374659447555, 87657516984, 87182202215, 80787, 19203926852, 179159], 'label': '77760.bo.180.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '180.co1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.co1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057034
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.x1', '90.be1', '90.bh1'], 'contains': ['360.co1', '360.co2', '360.cp2', '360.cq1', '360.cr1', '360.cx2', '360.cx3', '360.cy1', '360.dz2', '540.cz1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [461841090505, 462320323320, 143975, 19678982548, 80880, 80787, 143304], 'label': '77760.bo.180.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.cp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.cp1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057035
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.cp2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.x1', '90.bf1', '90.bg1'], 'contains': ['360.co1', '360.co2', '360.cp1', '360.cq2', '360.cr1', '360.cx1', '360.cy2', '360.dz1', '540.cz2'], 'core': '1440.b1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [448908278999, 143975, 19678982548, 80880, 80787, 462320328386, 143304], 'label': '77760.bo.180.cp2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.cp2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.cp2', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057036
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['20.f1', '90.w1', '90.bf1', '90.bh1'], 'contains': ['360.cp1', '360.cq1', '360.cu1', '360.cz1', '360.ea1', '540.da1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [87262035243, 83467916, 143975, 456053150130, 80880, 80787, 143304], 'label': '77760.bo.180.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.cq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.cq1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057037
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.v1', '90.bg1', '90.bh1'], 'contains': ['360.cp1', '360.cr1', '360.cv1', '360.dc1', '360.el1', '540.db1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [87182202116, 143975, 482768881, 80880, 80787, 375138230375, 143304], 'label': '77760.bo.180.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.cr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.cr1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057038
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.u1', '90.be1', '90.bi1'], 'contains': ['360.cp2', '360.cs1', '360.ct1', '360.de1', '360.df1', '360.en1', '360.eo1', '540.dc1', '540.de1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [462320323320, 143975, 19678982548, 80880, 80787, 7185202680, 143304], 'label': '77760.bo.180.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.cs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.cs1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057039
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.u1', '90.bh1'], 'contains': ['360.cp2', '360.cu1', '360.cv1', '360.dg1', '360.ep1', '540.dd1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [462320323320, 7185162389, 143975, 19678982548, 80880, 80787, 143304], 'label': '77760.bo.180.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.ct1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.ct1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057040
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.v1', '90.v1', '90.bf1', '90.bi1'], 'contains': ['360.cp1', '360.cs1', '360.cw1', '360.dd1', '360.dh1', '360.em1', '360.fh1', '540.df1', '540.dg1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [482808988, 87182202116, 143975, 80880, 80787, 375138230375, 143304], 'label': '77760.bo.180.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.cu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.cu1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057041
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.g1', '90.w1', '90.bg1', '90.bi1'], 'contains': ['360.cp1', '360.ct1', '360.db1', '360.di1', '360.eq1', '540.dh1', '540.di1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [87262035243, 83543730, 143975, 456053150130, 80880, 80787, 143304], 'label': '77760.bo.180.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.cv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.cv1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057042
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.u1', '90.x1', '90.bh1', '90.bi1'], 'contains': ['360.cp1', '360.cp2', '360.cw1', '360.da1', '360.da2', '360.dl1', '360.fk1', '540.dj1', '540.dk1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [448908278999, 462320323320, 143975, 19678982548, 80880, 80787, 143304], 'label': '77760.bo.180.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '180.cw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.cw1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057043
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.b1', '9.a1'], 'contains': ['36.b1', '36.q1', '36.s1', '54.a1', '108.b1', '180.b1', '270.c1'], 'core': '108.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [462320012159, 148, 93924236159, 5759], 'label': '77760.bo.18.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1', 'subgroup_fusion': None, 'weyl_group': '1440.5842'}
  • id: 246057044
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.v1', '90.be1', '90.bf1'], 'contains': ['360.cq1', '360.cr1', '360.cs1', '360.eb1', '360.ec1', '540.dr1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [87182202116, 143975, 375138270474, 482768881, 80880, 80787, 143304], 'label': '77760.bo.180.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.cx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.cx1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057045
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.u1', '90.bf1'], 'contains': ['360.cq2', '360.cs1', '360.cu1', '360.ee1', '360.eh1', '540.ds1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [143975, 80787, 7185202680, 143304, 19678982548, 80880, 462320328386], 'label': '77760.bo.180.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.cy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.cy1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057046
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.u1', '90.bg1', '90.bj1'], 'contains': ['360.cq2', '360.ct1', '360.cv1', '360.ef1', '360.eg1', '540.dt1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [143975, 80787, 7185162389, 143304, 19678982548, 80880, 462320328386], 'label': '77760.bo.180.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.cz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.cz1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057047
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.h1', '90.w1', '90.be1', '90.bj1'], 'contains': ['360.cq1', '360.ct1', '360.ej1', '360.ek1', '540.du1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [456053074316, 87262035243, 83467916, 143975, 80880, 80787, 143304], 'label': '77760.bo.180.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.da1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.da1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057048
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.y1', '90.be1', '90.bg1'], 'contains': ['360.cr1', '360.ct1', '360.es1', '360.et1', '540.dv1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [87182277597, 374659447555, 143975, 355938110909, 80880, 80787, 143304], 'label': '77760.bo.180.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.db1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.db1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057049
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.x1', '90.v1', '90.bh1', '90.bj1'], 'contains': ['360.cq1', '360.cv1', '360.cw1', '360.ed1', '360.ey1', '540.dx1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [143975, 80787, 143304, 180667209003, 443120250115, 442641300482, 80880], 'label': '77760.bo.180.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.dc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.dc1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057050
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.w1', '90.x1', '90.bf1', '90.bj1'], 'contains': ['360.cq1', '360.cq2', '360.cw1', '360.ei1', '360.fb1', '540.ea1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [461841004948, 143975, 19678982548, 80880, 80787, 462320328386, 143304], 'label': '77760.bo.180.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '180.dd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.dd1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057051
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.y1', '90.y1', '90.bf1', '90.bh1'], 'contains': ['360.cr1', '360.cu1', '360.cw1', '360.er1', '360.fn1', '540.eb1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [87182202116, 374659447555, 143975, 355938110909, 80880, 80787, 143304], 'label': '77760.bo.180.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.de1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.de1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057052
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.z1', '90.y1', '90.bi1', '90.bj1'], 'contains': ['360.ct1', '360.cw1', '360.eu1', '360.fr1', '360.fu1', '540.ee1', '540.ef1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [355938186480, 87182202116, 374659447555, 143975, 80880, 80787, 143304], 'label': '77760.bo.180.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.df1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.df1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057053
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.g1', '90.l1', '90.bh1'], 'contains': ['360.cy1', '360.da1', '360.dg1', '360.ea1', '360.ed1', '360.el1', '360.er1', '540.ei1', '540.en1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [448908278999, 461841090505, 462320323320, 143975, 19678982548, 80880, 80787], 'label': '77760.bo.180.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.dg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.dg1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057054
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.c1', '9.a1'], 'contains': ['36.b1', '36.u1', '36.w1', '54.b1', '108.c1', '180.c1', '270.d1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [148, 93924236159, 462320011466, 5759], 'label': '77760.bo.18.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
  • id: 246057055
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.dg2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.h1', '90.i1', '90.bh1'], 'contains': ['360.cz1', '360.da2', '360.dc1', '360.dz2', '360.ed1', '360.ep1', '360.er1', '540.ej1', '540.em1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841090505, 462320323891, 143975, 19678982548, 448908278667, 80880, 80787], 'label': '77760.bo.180.dg2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.dg2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.dg2', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057056
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.h1', '90.l1', '90.bg1'], 'contains': ['360.cy2', '360.db1', '360.dc1', '360.dz1', '360.eg1', '360.el1', '360.et1', '540.ek1', '540.eo1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841090505, 143975, 19678982548, 462320328958, 448908278667, 80880, 80787], 'label': '77760.bo.180.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.dh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.dh1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057057
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.i1', '90.l1', '90.bf1'], 'contains': ['360.cy2', '360.cz1', '360.dd1', '360.ec1', '360.eh1', '360.ei1', '360.er1', '540.ep1', '540.eq1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 461841148348, 19678982548, 448908278667, 80880, 80787, 462320328386], 'label': '77760.bo.180.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.di1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.di1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057058
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.g1', '90.n1', '90.be1'], 'contains': ['360.cy1', '360.de1', '360.eb1', '360.ej1', '360.es1', '540.el1', '540.es1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [462320323320, 143975, 19678982548, 461841188401, 80880, 80787, 448908283914], 'label': '77760.bo.180.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.dj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.dj1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057059
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.l1', '90.be1'], 'contains': ['360.cy1', '360.df1', '360.ec1', '360.ek1', '360.et1', '540.er1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [448908283441, 462320323320, 143975, 19678982548, 461841188401, 80880, 80787], 'label': '77760.bo.180.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.dk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.dk1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057060
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.g1', '90.bi1'], 'contains': ['360.da1', '360.de1', '360.em1', '360.eq1', '360.eu1', '540.et1', '540.eu1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [448908278999, 462320323320, 143975, 461841148348, 19678982548, 80880, 80787], 'label': '77760.bo.180.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.dl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.dl1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057061
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.bc1', '90.h1', '90.n1', '90.bf1'], 'contains': ['360.cy2', '360.cz1', '360.dh1', '360.eb1', '360.ee1', '360.fb1', '360.fn1', '540.ev1', '540.ew1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841004948, 143975, 19678982548, 448908278667, 80880, 80787, 462320328386], 'label': '77760.bo.180.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.dm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.dm1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057062
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.bd1', '90.h1', '90.bi1'], 'contains': ['360.da2', '360.db1', '360.dh1', '360.em1', '360.en1', '360.fk1', '360.fr1', '540.ex1', '540.ey1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [461841004948, 462320323891, 143975, 19678982548, 448908278667, 80880, 80787], 'label': '77760.bo.180.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.dn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.dn1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057063
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.i1', '90.n1', '90.bg1'], 'contains': ['360.cy2', '360.dc1', '360.di1', '360.ef1', '360.es1', '540.ez1', '540.fa1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [461841090505, 143975, 19678982548, 448908278667, 80880, 80787, 462320328386], 'label': '77760.bo.180.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.do1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.do1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057064
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.i1', '90.bi1'], 'contains': ['360.da2', '360.dd1', '360.di1', '360.eo1', '360.eu1', '540.fb1', '540.fc1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [462320323891, 143975, 461841148348, 19678982548, 448908278667, 80880, 80787], 'label': '77760.bo.180.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.dp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.dp1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057065
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '6.b1', '9.b1'], 'contains': ['36.a1', '36.e1', '36.t1', '54.a1', '108.e1', '180.h1', '270.p1'], 'core': '36.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [93924235466, 85805, 80787, 462320046985], 'label': '77760.bo.18.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '18.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
  • id: 246057066
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.ba1', '90.c1', '90.j1', '90.z1'], 'contains': ['360.dj1', '360.ew1', '360.fl1', '540.fd1', '540.fe1', '540.ff1', '540.fh1', '720.cn1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [355462813680, 462320052004, 87660966963, 482768881, 80880, 80787, 375138086400], 'label': '77760.bo.180.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.dq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.dq1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246057067
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.ba1', '90.k1'], 'contains': ['360.dk1', '360.ex1', '360.fm1', '540.fd1', '540.fi1', '720.co1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [461841004948, 462320052004, 19678982548, 262496684612, 80880, 80787, 448908283914], 'label': '77760.bo.180.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.k1', 'old_label': '180.dr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.dr1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
  • id: 246057068
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.ba1', '90.l1', '90.n1', '90.bh1'], 'contains': ['360.cy1', '360.cz1', '360.dc1', '360.dg1', '360.dl1', '360.ey1', '360.fn1', '540.fd1', '540.fg1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841004948, 462320323320, 143975, 19678982548, 80880, 80787, 448908283914], 'label': '77760.bo.180.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.ds1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.ds1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057069
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.ba1', '90.a1', '90.o1', '90.z1'], 'contains': ['360.dj1', '360.fc1', '360.fo1', '540.fg1', '540.fh1', '540.fi1', '540.fj1', '540.fk1', '720.cq1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [355462732800, 482849425, 462320323320, 143975, 87661002387, 80787, 375138230375], 'label': '77760.bo.180.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '180.dt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.dt1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246057070
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.bb1', '90.a1', '90.j1', '90.bb1'], 'contains': ['360.dj1', '360.ff1', '360.fp1', '540.fl1', '540.fn1', '540.fo1', '540.fq1', '720.cr1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [482808988, 355462732800, 462320323320, 143975, 87661002387, 80787, 375138230375], 'label': '77760.bo.180.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.du1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.du1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246057071
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.bb1', '90.k1'], 'contains': ['360.dk1', '360.fg1', '360.fq1', '540.fl1', '540.fo1', '540.fp1', '720.cs1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [448908278999, 262496649331, 462320323320, 19679028004, 143975, 461841050404, 80787], 'label': '77760.bo.180.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.k1', 'old_label': '180.dv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.dv1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057072
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.bb1', '90.l1', '90.bi1'], 'contains': ['360.da1', '360.db1', '360.dd1', '360.df1', '360.dl1', '360.fh1', '360.fr1', '540.fl1', '540.fm1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [462320323320, 143975, 461841148348, 19678982548, 448908278667, 80880, 80787], 'label': '77760.bo.180.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.dw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.dw1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057073
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.bb1', '90.bc1'], 'contains': ['360.dm1', '360.fi1', '360.fs1', '540.fm1', '540.fn1', '540.fp1', '540.fr1', '720.cu1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [448908278999, 262496649331, 462320323467, 19679028004, 461841050404, 80787, 179159], 'label': '77760.bo.180.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '180.dx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.dx1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057074
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.bb1'], 'contains': ['360.dn1', '360.fj1', '360.ft1', '540.fm1', '540.fo1', '540.fp1', '720.cv1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [448908278999, 462320323467, 19679028004, 461841050404, 262496684612, 80787, 179159], 'label': '77760.bo.180.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.dy1', 'old_label': '180.dy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.dy1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 246057075
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.bc1', '90.c1', '90.m1', '90.ba1'], 'contains': ['360.do1', '360.ev1', '360.fl1', '540.ev1', '540.fs1', '540.ft1', '720.cx1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [80787, 262496586387, 448908007104, 462320328958, 19678982548, 80880, 461841004948], 'label': '77760.bo.180.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.dz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.dz1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246057076
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '9.a1'], 'contains': ['36.f1', '36.q1', '36.u1', '54.a1', '108.f1', '180.i1', '270.q1'], 'core': '108.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93924235466, 5066, 80880, 462320011466], 'label': '77760.bo.18.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
  • id: 246057077
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.bc1', '90.b1', '90.o1', '90.ba1'], 'contains': ['360.do1', '360.ez1', '360.fo1', '540.ew1', '540.ft1', '540.fu1', '720.da1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [80787, 87660962042, 375138172205, 482635561, 355462813680, 80880, 462320046985], 'label': '77760.bo.180.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '180.ea1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.ea1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246057078
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.bd1', '90.b1', '90.m1', '90.bb1'], 'contains': ['360.do1', '360.fd1', '360.fp1', '540.ex1', '540.fv1', '540.fw1', '720.df1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [482808988, 375138167730, 355462732800, 462320323799, 87661065003, 143975, 80787], 'label': '77760.bo.180.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.eb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.eb1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246057079
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.bd1', '90.bc1'], 'contains': ['360.dp1', '360.fe1', '360.fs1', '540.ey1', '540.fv1', '540.fx1', '720.dg1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [262496649331, 462320323891, 19679028004, 461841050404, 448908278667, 80787, 179159], 'label': '77760.bo.180.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '180.ec1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.ec1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057080
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.be1', '90.n1', '90.bi1'], 'contains': ['360.de1', '360.dh1', '360.di1', '360.dl1', '360.fu1', '540.fy1', '540.fz1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [461841004948, 462320323320, 143975, 19678982548, 448908278667, 80880, 80787], 'label': '77760.bo.180.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.ed1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.ed1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057081
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.b1', '60.be1', '90.c1', '90.o1', '90.bb1'], 'contains': ['360.dj1', '360.do1', '360.gg1', '540.fy1', '540.ga1', '540.gb1', '720.dm1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [355462732800, 482676004, 462320323320, 143975, 87661002387, 80787, 375138230375], 'label': '77760.bo.180.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '180.ee1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.ee1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246057082
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.l1', '60.be1', '90.bc1'], 'contains': ['360.dm1', '360.dp1', '360.gh1', '540.fz1', '540.ga1', '540.gc1', '720.dn1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [355462732800, 482676004, 462320323467, 375138311012, 87661002387, 80787, 179159], 'label': '77760.bo.180.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.k1', 'old_label': '180.ef1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.ef1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057083
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.g1', '90.p1', '90.bg1'], 'contains': ['360.dz1', '360.ef1', '360.el1', '360.eq1', '360.es1', '540.gd1', '540.gf1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [448908278999, 461841090505, 143975, 19678982548, 462320328958, 80880, 80787], 'label': '77760.bo.180.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.eg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.eg1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057084
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.g1', '90.h1', '90.bf1'], 'contains': ['360.dz1', '360.ea1', '360.eb1', '360.ee1', '360.ei1', '360.em1', '360.er1', '540.gg1', '540.gh1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [448908278999, 143975, 461841148348, 19678982548, 80880, 80787, 462320328386], 'label': '77760.bo.180.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.eh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.eh1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057085
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.h1', '90.be1'], 'contains': ['360.dz2', '360.eb1', '360.ek1', '360.en1', '360.et1', '540.gi1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [461841090505, 448908283441, 462320323891, 143975, 19678982548, 80880, 80787], 'label': '77760.bo.180.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.ei1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.ei1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057086
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.i1', '90.p1', '90.be1'], 'contains': ['360.dz2', '360.ec1', '360.ej1', '360.eo1', '360.es1', '540.ge1', '540.gk1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [461841090505, 462320323891, 143975, 19678982548, 80880, 80787, 448908283914], 'label': '77760.bo.180.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.ej1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.ej1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057088
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.g1', '90.i1', '90.bj1'], 'contains': ['360.ed1', '360.ef1', '360.ei1', '360.ej1', '360.eu1', '540.gj1', '540.gl1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [143975, 461841148348, 19678982548, 80880, 80787, 448908283914, 462320328386], 'label': '77760.bo.180.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.ek1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.ek1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057089
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.bf1', '90.a1', '90.q1', '90.ba1'], 'contains': ['360.ev1', '360.ff1', '360.fo1', '540.gm1', '540.gq1', '540.gr1', '540.gs1', '720.ez1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [448908278999, 461841004948, 19678982548, 462320328958, 262496586387, 80880, 80787], 'label': '77760.bo.180.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.el1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.el1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246057090
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.bg1', '90.b1', '90.q1', '90.z1'], 'contains': ['360.ew1', '360.fd1', '360.fo1', '540.gn1', '540.go1', '540.gp1', '540.gu1', '720.fc1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [87661238852, 375138449015, 462320323891, 482635561, 355462813680, 80880, 80787], 'label': '77760.bo.180.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.em1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.em1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246057091
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.bg1', '90.h1', '90.p1', '90.bh1'], 'contains': ['360.dz2', '360.ea1', '360.el1', '360.ep1', '360.ey1', '360.fk1', '360.fn1', '540.gn1', '540.gv1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841004948, 462320323891, 143975, 19678982548, 80880, 80787, 448908283914], 'label': '77760.bo.180.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.en1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.en1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057092
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.bf1', '90.d1', '90.j1', '90.ba1'], 'contains': ['360.ez1', '360.ff1', '360.fl1', '540.gr1', '540.gt1', '540.hd1', '720.ff1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 461841050404, 80787, 19679028004, 462320328958, 262496684612, 448908278999], 'label': '77760.bo.180.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.eo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.eo1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246057093
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.bf1', '90.k1'], 'contains': ['360.fa1', '360.fg1', '360.fm1', '540.gs1', '540.hd1', '720.fg1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [143975, 80787, 375138172555, 87661059842, 482635561, 462320328958, 355462813680], 'label': '77760.bo.180.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.k1', 'old_label': '180.ep1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.ep1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
  • id: 246057094
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.bf1', '90.l1', '90.p1', '90.bf1'], 'contains': ['360.dz1', '360.ea1', '360.ec1', '360.eh1', '360.fb1', '360.fh1', '360.fn1', '540.gq1', '540.hd1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [448908278999, 461841004948, 143975, 19678982548, 80880, 80787, 462320328386], 'label': '77760.bo.180.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.eq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.eq1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057095
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.bg1', '90.d1', '90.m1', '90.z1'], 'contains': ['360.fc1', '360.fd1', '360.fl1', '540.gu1', '540.gv1', '540.gw1', '540.gx1', '720.fr1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [462320323891, 19679028004, 143975, 448908284158, 461841050404, 262496684612, 80787], 'label': '77760.bo.180.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.er1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.er1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246057096
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.bh1', '90.b1', '90.j1', '90.bd1'], 'contains': ['360.ew1', '360.ez1', '360.fp1', '540.gy1', '540.hb1', '540.he1', '720.fl1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [482808988, 355462732800, 87661059842, 143975, 462320328958, 375138172555, 80787], 'label': '77760.bo.180.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.es1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.es1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246057097
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.bh1', '90.k1'], 'contains': ['360.ex1', '360.fa1', '360.fq1', '540.hc1', '540.he1', '720.fm1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [482808988, 87660962042, 355462911959, 375138172205, 80880, 80787, 462320046985], 'label': '77760.bo.180.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.k1', 'old_label': '180.et1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.et1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
  • id: 246057098
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.c1', '6.d1', '9.b1'], 'contains': ['36.e1', '36.t1', '36.v1', '54.b1', '108.h1', '180.n1', '270.t1'], 'core': '72.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93924235466, 462320328958, 85805, 80787], 'label': '77760.bo.18.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
  • id: 246057099
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.bh1', '90.h1', '90.l1', '90.bj1'], 'contains': ['360.ed1', '360.eg1', '360.ei1', '360.ek1', '360.ey1', '360.fb1', '360.fr1', '540.ha1', '540.he1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841004948, 143975, 19678982548, 80880, 80787, 448908283914, 462320328386], 'label': '77760.bo.180.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.eu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.eu1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057100
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.bh1', '90.a1', '90.m1', '90.bd1'], 'contains': ['360.ev1', '360.fc1', '360.fp1', '540.gz1', '540.ha1', '540.hb1', '540.hc1', '720.fs1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [482808988, 87661140722, 462320225425, 355462813680, 375138270245, 80880, 80787], 'label': '77760.bo.180.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.ev1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.ev1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246057101
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.bi1', '90.n1', '90.p1', '90.bj1'], 'contains': ['360.ef1', '360.ej1', '360.ey1', '360.fb1', '360.fu1', '540.hf1', '540.hg1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [461841004948, 448908283441, 143975, 19678982548, 80880, 80787, 462320328386], 'label': '77760.bo.180.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.ew1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.ew1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057102
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.bj1', '90.p1', '90.bi1'], 'contains': ['360.eo1', '360.eq1', '360.fh1', '360.fk1', '360.fu1', '540.hh1', '540.hi1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [448908278999, 461841004948, 462320323891, 143975, 19678982548, 80880, 80787], 'label': '77760.bo.180.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '180.ex1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.ex1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057103
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.m1', '60.bi1', '90.c1', '90.q1', '90.bd1'], 'contains': ['360.ev1', '360.ew1', '360.gg1', '540.hf1', '540.hj1', '540.hk1', '720.eb1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841004948, 19678982548, 462320328958, 262496586387, 80880, 80787, 448908283914], 'label': '77760.bo.180.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.ey1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.ey1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246057104
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.c1', '60.bi1', '90.d1', '90.o1', '90.bd1'], 'contains': ['360.ez1', '360.fc1', '360.gg1', '540.hg1', '540.hk1', '540.hl1', '720.ec1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [461841004948, 448908001949, 19678982548, 262496586387, 80880, 80787, 462320046985], 'label': '77760.bo.180.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '180.ez1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.ez1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246057105
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.n1', '60.bj1', '90.d1', '90.q1', '90.bb1'], 'contains': ['360.fd1', '360.ff1', '360.gg1', '540.hh1', '540.hm1', '540.hn1', '720.ed1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [462320323799, 461841050404, 143975, 80787, 19679028004, 262496684612, 448908278999], 'label': '77760.bo.180.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.fa1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.fa1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246057187
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '18.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.i1', '9.a1'], 'contains': ['36.o1', '36.s1', '36.u1', '54.g1', '108.q1', '180.cm1', '270.cb1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [93924231093, 143975, 462320328386, 143304], 'label': '77760.bo.18.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.n1', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
  • id: 246057106
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '180.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.o1', '60.bj1', '90.bc1'], 'contains': ['360.fe1', '360.fi1', '360.gh1', '540.hi1', '540.hm1', '540.ho1', '720.ee1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [448908278999, 462320323799, 262496649331, 19679028004, 461841050404, 80787, 179159], 'label': '77760.bo.180.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '180.fb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.fb1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057107
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '216.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.a1', 'complements': ['360.bs1', '360.bb2', '360.co2', '360.bb1', '360.cx1', '360.cx3', '360.co1', '360.cx2', '360.ba1'], 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '72.q1', '72.r1', '108.a1', '108.d1', '108.n1', '108.r1', '108.s1'], 'contains': ['1296.w1', '2160.fm1', '3240.if1'], 'core': '216.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [274511462400, 87181920000], 'label': '77760.bo.216.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': ['72.a1', '108.a1'], 'normal_contains': ['77760.a1'], 'normalizer': '1.a1', 'old_label': '216.a1', 'projective_image': '77760.bo', 'quotient_action_image': '2.1', 'quotient_action_kernel': '108.17', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '216.a1', 'subgroup_fusion': None, 'weyl_group': '720.763'}
  • id: 246057108
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.b1', '72.b1', '108.b1', '108.c1', '108.i1'], 'contains': ['432.p1', '648.c1', '1080.h1', '1296.a1', '2160.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [143975, 286483093054, 40585, 25470766654], 'label': '77760.bo.216.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1', 'subgroup_fusion': None, 'weyl_group': '240.189'}
  • id: 246057109
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.e1', '9.a1'], 'contains': ['36.b1', '36.f1', '36.o1', '54.c1', '108.i1', '180.q1', '270.w1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87182277597, 274511462400, 143975, 5066, 143304], 'label': '77760.bo.18.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
  • id: 246057110
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.c1', '72.c1', '108.k1'], 'contains': ['432.a1', '432.i1', '432.j1', '648.a1', '648.d1', '1080.x1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [86155, 267841769035, 269202533759, 80880, 80787, 181146153355], 'label': '77760.bo.216.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '216.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 246057111
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.d1', '72.d1', '108.k1'], 'contains': ['432.a1', '432.k1', '432.l1', '648.b1', '648.e1', '1080.ba1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [269202666957, 143975, 267842049986, 85805, 80787, 181146153355], 'label': '77760.bo.216.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '216.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 246057112
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.e1', '72.b1', '72.e1', '108.e1', '108.h1', '108.j1'], 'contains': ['432.o1', '648.c1', '1080.bf1', '1296.c1', '2160.v1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [286482914185, 85805, 25470587785, 80787], 'label': '77760.bo.216.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '216.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 246057113
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.f1', '72.e1', '108.f1', '108.g1', '108.i1'], 'contains': ['432.p1', '648.c1', '1080.bh1', '1296.d1', '2160.w1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [40585, 286482914185, 25470587785, 80880], 'label': '77760.bo.216.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 246057114
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.g1', '72.c1', '108.k1'], 'contains': ['432.c1', '432.i1', '432.k1', '648.d1', '648.f1', '1080.br1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [80787, 85805, 269202533066, 181146153005, 267841768349, 80880], 'label': '77760.bo.216.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '216.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.g1', 'subgroup_fusion': None, 'weyl_group': '2160.cr'}
  • id: 246057115
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.h1', '72.d1', '108.k1'], 'contains': ['432.c1', '432.j1', '432.l1', '648.e1', '648.g1', '1080.bu1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [183845, 267842050558, 143975, 181146251274, 269202533759, 80787], 'label': '77760.bo.216.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '216.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.h1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 246057116
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.i1', '72.f1', '108.k1'], 'contains': ['432.a1', '432.b1', '432.c1', '432.d1', '432.e1', '432.f1', '432.h1', '648.h1', '648.i1', '1080.by1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1037980104, 143975, 85805, 80787, 18764663042, 143304], 'label': '77760.bo.216.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '216.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.i1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 246057117
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.k1', '72.g1', '72.h1', '108.j1', '108.l1', '108.m1'], 'contains': ['432.o1', '648.l1', '1080.cg1', '1296.i1', '2160.bs1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [349232083893, 455574148294, 80787, 693], 'label': '77760.bo.216.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.j1', 'subgroup_fusion': None, 'weyl_group': '240.189'}
  • id: 246057118
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '216.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.l1', '72.i1', '108.k1'], 'contains': ['432.f1', '432.i1', '432.l1', '648.j1', '648.m1', '1080.cu1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [181146067893, 269202609094, 267841773813, 80880, 80787, 693], 'label': '77760.bo.216.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '216.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.k1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 246057119
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '216.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.n1', '72.j1', '108.k1'], 'contains': ['432.f1', '432.j1', '432.k1', '648.k1', '648.n1', '1080.cx1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [267842045491, 143975, 269202609094, 80787, 181146153355, 143304], 'label': '77760.bo.216.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '216.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.l1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 246057120
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '9.b1'], 'contains': ['36.e1', '36.k1', '54.c1', '108.j1', '180.s1', '270.z1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [87182277597, 362615, 274511462400, 85805, 80787], 'label': '77760.bo.18.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
  • id: 246057121
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '216.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.m1', '72.i1'], 'contains': ['432.g1', '432.m1', '432.n1', '648.j1', '648.o1', '1080.cy1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [181146067893, 267842045252, 224184, 269202609094, 80787, 179159], 'label': '77760.bo.216.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.m1', 'old_label': '216.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.m1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246057122
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '216.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.o1', '72.g1', '108.i1', '108.o1', '108.q1'], 'contains': ['432.p1', '648.l1', '1080.dd1', '1296.k1', '2160.cl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [455574067893, 349232083893, 148, 693], 'label': '77760.bo.216.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '216.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.n1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 246057123
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '216.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.p1', '72.h1', '108.p1'], 'contains': ['432.q1', '648.l1', '1080.df1', '1296.l1', '2160.cm1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [25470690931, 143731, 286483017331, 143304], 'label': '77760.bo.216.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.m1', 'old_label': '216.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.o1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 246057124
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '216.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.a1', '72.k1', '72.l1', '108.e1', '108.l1'], 'contains': ['432.o1', '648.p1', '1080.en1', '1296.n1', '2160.dx1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [174879129600, 462320052004, 80787], 'label': '77760.bo.216.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '216.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.p1', 'subgroup_fusion': None, 'weyl_group': '240.189'}
  • id: 246057125
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '216.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.q1', '72.k1', '108.b1', '108.f1', '108.o1'], 'contains': ['432.p1', '648.p1', '1080.eo1', '1296.q1', '2160.dy1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [479363787, 443555843787, 143975], 'label': '77760.bo.216.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '216.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.q1', 'subgroup_fusion': None, 'weyl_group': '240.189'}
  • id: 246057128
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '216.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.t1', '72.m1', '72.n1', '108.e1', '108.h1', '108.m1'], 'contains': ['432.o1', '648.q1', '1080.gr1', '1296.o1', '2160.ew1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [174879406650, 462320328958, 80787], 'label': '77760.bo.216.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '216.t1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.t1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 246057129
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '216.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.u1', '72.n1', '108.c1', '108.f1', '108.q1'], 'contains': ['432.p1', '648.q1', '1080.gt1', '1296.s1', '2160.ex1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [479278650, 143975, 443555758650], 'label': '77760.bo.216.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '216.u1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.u1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 246057130
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '216.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.v1', '72.o1', '72.p1', '108.h1', '108.l1'], 'contains': ['432.o1', '648.r1', '1080.gz1', '1296.p1', '2160.ey1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [479364452, 443555763571, 80787], 'label': '77760.bo.216.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.v1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.v1', 'subgroup_fusion': None, 'weyl_group': '240.189'}
  • id: 246057131
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': ['38880.g1', '38880.a1', '38880.e1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.c1', '4.e1', '6.g1', '6.h1', '12.j1', '20.g1', '30.k1'], 'core': '2.d1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [93924311494, 462320323320, 143975, 80880, 80787, 143304], 'label': '77760.bo.2.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.c1', '4.e1'], 'normalizer': '1.a1', 'old_label': '2.d1', 'projective_image': '77760.bo', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1', 'subgroup_fusion': None, 'weyl_group': '25920.w'}
  • id: 246057132
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3.a1', '6.f1'], 'contains': ['36.c1', '36.d1', '36.g1', '36.h1', '36.i1', '36.l1', '36.n1', '54.d1', '54.e1', '90.s1', '108.k1', '180.bt1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [174879492452, 362615, 85805, 80880, 80787, 462320046985], 'label': '77760.bo.18.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '18.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1', 'subgroup_fusion': None, 'weyl_group': '4320.bp'}
  • id: 246057133
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '216.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.w1', '72.o1', '108.c1', '108.g1', '108.o1'], 'contains': ['432.p1', '648.r1', '1080.hi1', '1296.t1', '2160.ez1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [174879492215, 143975, 462320369015], 'label': '77760.bo.216.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '216.w1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.w1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 246057134
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '216.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.x1', '72.p1', '108.p1'], 'contains': ['432.q1', '648.r1', '1080.hj1', '1296.v1', '2160.fa1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [174879492215, 462320369015, 179159], 'label': '77760.bo.216.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.m1', 'old_label': '216.x1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.x1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 246057135
    {'ambient': '77760.bo', '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': '8640.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['80.a1', '120.a1', '120.b1', '120.q1'], 'contains': ['480.a1', '480.j1', '480.r1', '720.b1', '720.f1', '720.g1', '720.h1', '720.i1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [86155, 456053074316, 93448857748, 174400173363, 80880, 80787], 'label': '77760.bo.240.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '240.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.a1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057136
    {'ambient': '77760.bo', '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': '25920.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.b1', '120.b1', '120.c1', '120.d1', '120.e1', '120.r1'], 'contains': ['480.a1', '480.o1', '480.bd1', '720.c1', '720.k1', '720.l1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [183845, 280259700485, 482768881, 80880, 80787, 193999357587], 'label': '77760.bo.240.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '240.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.b1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 246057137
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['80.c1', '120.a1', '120.c1', '120.q1'], 'contains': ['480.a1', '480.u1', '480.x1', '720.d1', '720.o1', '720.p1', '720.q1', '720.r1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [40349, 174400208787, 93449036612, 83543730, 143975, 80787], 'label': '77760.bo.240.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '240.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.c1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 246057138
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.d1', '120.a1', '120.r1'], 'contains': ['480.a1', '480.bf1', '480.bh1', '720.e1', '720.t1', '720.u1', '720.v1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [183845, 482635561, 280259700485, 80880, 80787, 193999357587], 'label': '77760.bo.240.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '240.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.d1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246057139
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.n1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.d1', '80.a1', '120.f1', '120.j1', '120.s1'], 'contains': ['480.d1', '480.h1', '480.s1', '720.f1', '720.y1', '720.z1', '720.ba1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [183845, 174436599746, 143975, 375138172555, 80880, 80787], 'label': '77760.bo.240.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '240.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.e1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057140
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['80.a1', '120.g1'], 'contains': ['480.b1', '480.i1', '480.t1', '720.h1', '720.z1', '720.bb1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 160, 'diagramx': None, 'generators': [183845, 174400208787, 93449001331, 456053154955, 143975, 80787], 'label': '77760.bo.240.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.a1', 'old_label': '240.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.f1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057141
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['80.a1', '120.h1', '120.k1', '120.q1'], 'contains': ['480.c1', '480.j1', '480.u1', '720.i1', '720.j1', '720.y1', '720.bb1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 80, 'diagramx': None, 'generators': [93448857748, 83543044, 174400173363, 85805, 80880, 80787], 'label': '77760.bo.240.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '240.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.g1', 'subgroup_fusion': None, 'weyl_group': '1296.2985'}
  • id: 246057142
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.e1', '80.a1', '120.i1', '120.j1', '120.t1'], 'contains': ['480.d1', '480.k1', '480.v1', '720.g1', '720.ba1', '720.bb1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 80, 'diagramx': None, 'generators': [143975, 375138270474, 188331136563, 85805, 80880, 80787], 'label': '77760.bo.240.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '240.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.h1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057143
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1', '6.h1', '9.b1'], 'contains': ['36.a1', '36.k1', '36.v1', '54.f1', '108.l1', '180.ca1', '270.bn1'], 'core': '36.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93924311494, 462320052004, 80787, 693], 'label': '77760.bo.18.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.j1', 'subgroup_fusion': None, 'weyl_group': '1440.5842'}
  • id: 246057144
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.b1', '60.l1', '80.b1', '120.j1', '120.l1', '120.u1'], 'contains': ['480.d1', '480.n1', '480.be1', '720.k1', '720.bc1', '720.bd1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [88176350010, 143975, 85805, 80880, 80787, 113567005680], 'label': '77760.bo.240.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '240.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.i1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057145
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.b1', '120.k1', '120.n1', '120.o1', '120.p1', '120.r1'], 'contains': ['480.c1', '480.o1', '480.bf1', '720.l1', '720.m1', '720.bd1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [183845, 482849425, 143975, 193999455812, 280259665445, 80787], 'label': '77760.bo.240.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '240.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.j1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246057146
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['80.c1', '120.g1'], 'contains': ['480.b1', '480.q1', '480.w1', '720.p1', '720.be1', '720.bg1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [174400352612, 93449001331, 83543730, 85805, 80880, 80787], 'label': '77760.bo.240.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.g1', 'old_label': '240.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.k1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057147
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['80.c1', '120.h1', '120.n1', '120.q1'], 'contains': ['480.c1', '480.r1', '480.x1', '720.n1', '720.q1', '720.be1', '720.bf1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [183845, 456053207518, 174400208787, 93449036612, 143975, 80787], 'label': '77760.bo.240.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '240.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.l1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 246057148
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.n1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.h1', '80.c1', '120.i1', '120.l1', '120.s1'], 'contains': ['480.d1', '480.s1', '480.y1', '720.o1', '720.be1', '720.bh1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [183845, 174436599746, 143975, 375138270474, 80880, 80787], 'label': '77760.bo.240.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '240.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.m1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057149
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.i1', '80.c1', '120.f1', '120.l1', '120.t1'], 'contains': ['480.d1', '480.v1', '480.bb1', '720.r1', '720.bf1', '720.bg1', '720.bh1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 80, 'diagramx': None, 'generators': [183845, 442641386755, 143975, 442162067904, 80880, 80787], 'label': '77760.bo.240.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '240.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.n1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057150
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['80.d1', '120.g1'], 'contains': ['480.b1', '480.bc1', '480.bg1', '720.u1', '720.bi1', '720.bj1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [280259521949, 193999455812, 482768881, 85805, 80880, 80787], 'label': '77760.bo.240.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.g1', 'old_label': '240.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.o1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057151
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.d1', '120.h1', '120.r1'], 'contains': ['480.c1', '480.bd1', '480.bh1', '720.s1', '720.v1', '720.bi1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [183845, 482635561, 143975, 193999455812, 280259665445, 80787], 'label': '77760.bo.240.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '240.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.p1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246057152
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.j1', '80.d1', '120.f1', '120.i1', '120.u1'], 'contains': ['480.d1', '480.be1', '480.bi1', '720.t1', '720.bi1', '720.bj1', '720.bk1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [143975, 80787, 368392286010, 442637676988, 183845, 80880], 'label': '77760.bo.240.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '240.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.q1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057153
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.e1', '120.q1', '120.r1'], 'contains': ['480.a1', '480.c1', '480.e1', '720.w1', '720.x1', '720.bl1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [193999357894, 280259567405, 143975, 85805, 80787, 143304], 'label': '77760.bo.240.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '240.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.r1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 246057154
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '18.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1', '9.b1'], 'contains': ['36.k1', '36.t1', '54.g1', '108.m1', '180.cb1', '270.bo1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [93924311494, 80787, 462320046985, 693], 'label': '77760.bo.18.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.k1', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
  • id: 246057155
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.p1', '80.e1', '120.s1', '120.t1', '120.u1'], 'contains': ['480.d1', '480.g1', '720.a1', '720.bl1'], 'core': '720.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [355419504452, 143975, 85805, 80880, 80787, 143304], 'label': '77760.bo.240.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '240.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.s1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057156
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['80.f1', '120.q1', '120.v1', '120.w1'], 'contains': ['480.e1', '480.j1', '480.x1', '720.bm1', '720.bq1', '720.bs1', '720.bu1', '720.bv1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [93448857748, 83543730, 174400173363, 80880, 80787, 693], 'label': '77760.bo.240.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '240.t1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.t1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057157
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.f1', '120.x1'], 'contains': ['480.f1', '480.m1', '480.ba1', '720.bm1', '720.br1', '720.bt1', '720.bw1', '720.bx1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [174400208787, 93449001331, 178680, 456053150130, 80787, 179159], 'label': '77760.bo.240.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.x1', 'old_label': '240.u1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.u1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057158
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.g1', '120.r1', '120.w1', '120.y1', '120.z1', '120.ba1'], 'contains': ['480.e1', '480.o1', '480.bh1', '720.bn1', '720.by1', '720.ca1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [482808988, 280259481600, 224184, 143975, 193999322613, 80787], 'label': '77760.bo.240.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '240.v1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.v1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 246057159
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.g1', '120.x1', '120.bb1'], 'contains': ['480.f1', '480.p1', '480.bk1', '720.bn1', '720.bz1', '720.cb1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [482808988, 193999357894, 280259481600, 224184, 80787, 179159], 'label': '77760.bo.240.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.s1', 'old_label': '240.w1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.w1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057160
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['80.h1', '120.q1', '120.v1', '120.y1'], 'contains': ['480.e1', '480.r1', '480.u1', '720.bo1', '720.cc1', '720.cd1', '720.ce1', '720.cf1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [174400208787, 93449036612, 456053154955, 143975, 80787, 143304], 'label': '77760.bo.240.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '240.x1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.x1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 246057161
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.i1', '120.r1', '120.v1'], 'contains': ['480.e1', '480.bd1', '480.bf1', '720.bp1', '720.cg1', '720.ch1', '720.ci1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [193999357894, 280259481600, 482849425, 143975, 80787, 143304], 'label': '77760.bo.240.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '240.y1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.y1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246057162
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.u1', '80.f1', '120.s1', '120.bc1', '120.be1'], 'contains': ['480.g1', '480.h1', '480.y1', '720.bq1', '720.br1', '720.cj1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [143975, 174436559403, 80880, 80787, 375138230375, 143304], 'label': '77760.bo.240.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '240.z1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.z1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057163
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.v1', '80.f1', '120.t1', '120.bd1', '120.be1'], 'contains': ['480.g1', '480.k1', '480.bb1', '720.bs1', '720.bt1', '720.cj1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [188331315147, 143975, 80880, 80787, 375138230375, 143304], 'label': '77760.bo.240.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '240.ba1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.ba1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057164
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.c1', '60.z1', '80.g1', '120.u1', '120.be1', '120.bf1'], 'contains': ['480.g1', '480.n1', '480.bi1', '720.by1', '720.bz1', '720.ck1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [88176292437, 143975, 80880, 80787, 113567005680, 143304], 'label': '77760.bo.240.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '240.bb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bb1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057165
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '18.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.g1', '9.a1'], 'contains': ['36.o1', '36.q1', '36.w1', '54.f1', '108.o1', '180.ch1', '270.by1'], 'core': '108.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [93924231093, 462320006400, 148, 693], 'label': '77760.bo.18.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '18.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.l1', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
  • id: 246057166
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.w1', '80.h1', '120.s1', '120.bd1', '120.bf1'], 'contains': ['480.g1', '480.s1', '720.cc1', '720.cl1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [143975, 375138270474, 174436559403, 80880, 80787, 143304], 'label': '77760.bo.240.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '240.bc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bc1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057167
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.x1', '80.h1', '120.t1', '120.bc1', '120.bf1'], 'contains': ['480.g1', '480.v1', '720.cf1', '720.cl1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [188331315147, 143975, 375138270474, 80880, 80787, 143304], 'label': '77760.bo.240.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '240.bd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bd1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057168
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.y1', '80.i1', '120.u1', '120.bc1', '120.bd1'], 'contains': ['480.g1', '480.be1', '720.cg1', '720.cm1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [368392152811, 143975, 442637676988, 80880, 80787, 143304], 'label': '77760.bo.240.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '240.be1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.be1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057169
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.ba1', '80.j1', '120.f1', '120.j1', '120.bc1'], 'contains': ['480.h1', '480.v1', '480.be1', '720.cn1', '720.co1', '720.cp1', '720.cq1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [143975, 80787, 519235320, 442641386424, 997961035, 80880], 'label': '77760.bo.240.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '240.bf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bf1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057170
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.bb1', '80.k1', '120.f1', '120.be1'], 'contains': ['480.h1', '480.bb1', '480.bi1', '720.cr1', '720.cs1', '720.ct1', '720.cu1', '720.cv1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [442641386424, 143975, 997965813, 519235320, 80880, 80787], 'label': '77760.bo.240.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '240.bg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bg1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057171
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['80.j1', '120.g1'], 'contains': ['480.i1', '480.q1', '480.bc1', '720.co1', '720.cx1', '720.db1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [174400352612, 456053074316, 93448857748, 180587273035, 80880, 80787], 'label': '77760.bo.240.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.g1', 'old_label': '240.bh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bh1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057172
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['80.j1', '120.b1', '120.h1', '120.v1'], 'contains': ['480.j1', '480.r1', '480.bd1', '720.cn1', '720.cx1', '720.cy1', '720.cz1', '720.dc1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [456053074316, 93448857748, 174400173363, 180587273035, 80880, 80787], 'label': '77760.bo.240.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '240.bi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bi1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 246057173
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.bc1', '80.j1', '120.i1', '120.j1', '120.bd1'], 'contains': ['480.k1', '480.s1', '480.be1', '720.cp1', '720.cx1', '720.da1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [143975, 174436416243, 375138270474, 368871328051, 80880, 80787], 'label': '77760.bo.240.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '240.bj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bj1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057174
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['80.j1', '120.a1', '120.k1', '120.v1'], 'contains': ['480.j1', '480.u1', '480.bf1', '720.cq1', '720.da1', '720.db1', '720.dc1', '720.dd1', '720.de1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 80, 'diagramx': None, 'generators': [93448857748, 174400173363, 456053149444, 180587272349, 80880, 80787], 'label': '77760.bo.240.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '240.bk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bk1', 'subgroup_fusion': None, 'weyl_group': '3888.ik'}
  • id: 246057175
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['80.k1', '120.g1'], 'contains': ['480.i1', '480.w1', '480.bg1', '720.cs1', '720.df1', '720.dh1', '720.di1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [180587456184, 83606375, 143975, 174400173363, 93449081975, 80787], 'label': '77760.bo.240.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.g1', 'old_label': '240.bl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bl1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057176
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1'], 'contains': ['36.p1', '36.r1', '36.x1', '54.f1', '108.p1', '180.ci1', '270.bz1'], 'core': '108.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [93924231093, 224184, 462320323467, 224612], 'label': '77760.bo.18.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '18.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.m1', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
  • id: 246057177
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['80.k1', '120.a1', '120.h1', '120.w1'], 'contains': ['480.j1', '480.x1', '480.bh1', '720.cr1', '720.df1', '720.dh1', '720.dj1', '720.dk1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [93448857748, 180587277813, 174400173363, 456053150130, 80880, 80787], 'label': '77760.bo.240.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '240.bm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bm1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 246057178
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.bd1', '80.k1', '120.i1', '120.be1'], 'contains': ['480.k1', '480.y1', '480.bi1', '720.ct1', '720.df1', '720.dg1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [375138087093, 143975, 174436416243, 368871328051, 80880, 80787], 'label': '77760.bo.240.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '240.bn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bn1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057179
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.k1'], 'contains': ['480.l1', '480.z1', '480.bj1', '720.cv1', '720.dg1', '720.dh1', '720.di1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [180587410680, 93449001331, 174400173363, 456053150130, 80787, 179159], 'label': '77760.bo.240.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.bo1', 'old_label': '240.bo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bo1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 246057180
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.k1', '120.x1'], 'contains': ['480.m1', '480.ba1', '480.bk1', '720.cu1', '720.dg1', '720.di1', '720.dj1', '720.dl1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [180587456184, 174400208787, 93449001331, 83687012, 80787, 179159], 'label': '77760.bo.240.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.x1', 'old_label': '240.bp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bp1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057181
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.d1', '60.be1', '80.l1', '120.j1', '120.be1'], 'contains': ['480.h1', '480.k1', '480.n1', '720.cw1', '720.dm1', '720.dn1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [143975, 174436416243, 368871328051, 80880, 80787, 375138230375], 'label': '77760.bo.240.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '240.bq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bq1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057182
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['80.l1', '120.b1', '120.k1', '120.w1', '120.bj1', '120.bk1', '120.bl1', '120.bn1'], 'contains': ['480.j1', '480.o1', '720.dm1', '720.do1', '720.dp1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [180587277504, 93448857748, 174400173363, 456053149444, 80880, 80787], 'label': '77760.bo.240.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '240.br1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.br1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 246057183
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.l1', '120.x1', '120.bm1', '120.bo1'], 'contains': ['480.m1', '480.p1', '720.dn1', '720.do1', '720.dq1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [174400208787, 93449001331, 83687012, 180587232000, 80787, 179159], 'label': '77760.bo.240.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.g1', 'old_label': '240.bs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bs1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057184
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.e1', '60.bi1', '80.m1', '120.j1', '120.l1', '120.bf1'], 'contains': ['480.n1', '480.s1', '480.v1', '720.dr1', '720.eb1', '720.ec1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [368871287518, 143975, 174436416243, 375138270474, 80880, 80787], 'label': '77760.bo.240.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '240.bt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bt1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057185
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.f1', '60.bj1', '80.n1', '120.l1', '120.be1'], 'contains': ['480.n1', '480.y1', '480.bb1', '720.ds1', '720.ed1', '720.ee1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [442641386755, 143975, 997965813, 519235320, 80880, 80787], 'label': '77760.bo.240.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '240.bu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bu1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057186
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.a1', '120.m1', '120.bg1', '120.bh1', '120.bi1', '120.bp1', '120.bq1', '120.br1', '120.bs1', '120.bt1', '120.bu1', '120.cc1'], 'contains': ['720.ef1', '720.eg1', '720.eh1', '720.ei1', '720.ej1', '960.c1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [355499200051, 143975, 355419504028, 442681021680, 80880, 80787], 'label': '77760.bo.240.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '240.bv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bv1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246057188
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['80.m1', '120.b1', '120.n1', '120.y1', '120.bj1', '120.bv1', '120.bw1', '120.by1'], 'contains': ['480.o1', '480.r1', '720.eb1', '720.ek1', '720.el1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [180587277504, 93448857748, 83467916, 174400173363, 80880, 80787], 'label': '77760.bo.240.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '240.bw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bw1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 246057189
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['80.m1', '120.c1', '120.k1', '120.y1', '120.bk1', '120.bx1', '120.by1', '120.bz1'], 'contains': ['480.o1', '480.u1', '720.ec1', '720.el1', '720.em1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [143975, 80787, 174400208787, 83548555, 93449036612, 180587232000], 'label': '77760.bo.240.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '240.bx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bx1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246057190
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['80.n1', '120.c1', '120.n1', '120.w1', '120.bl1', '120.bv1', '120.bx1', '120.ca1'], 'contains': ['480.o1', '480.x1', '720.ed1', '720.en1', '720.eo1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [180587277504, 93448857748, 83543730, 174400173363, 80880, 80787], 'label': '77760.bo.240.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '240.by1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.by1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 246057191
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.n1', '120.x1', '120.bm1', '120.cb1'], 'contains': ['480.p1', '480.ba1', '720.ee1', '720.en1', '720.ep1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [174400208787, 93449001331, 83543730, 180587232000, 80787, 179159], 'label': '77760.bo.240.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.s1', 'old_label': '240.bz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bz1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057192
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.a1', '80.o1', '120.d1', '120.o1', '120.z1', '120.bn1', '120.bw1', '120.bz1', '120.ca1'], 'contains': ['480.o1', '720.eq1', '720.et1', '2160.ek1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [482711044, 88695175204, 280259527104, 80880, 80787, 193999357587], 'label': '77760.bo.240.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '240.ca1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.ca1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 246057193
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.p1', '120.e1', '120.p1', '120.z1', '120.bl1', '120.by1'], 'contains': ['480.o1', '720.er1', '720.eu1', '2160.el1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [482711044, 88695353644, 280259527104, 80880, 80787, 193999357587], 'label': '77760.bo.240.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '240.cb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.cb1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 246057194
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.q1', '120.d1', '120.p1', '120.ba1', '120.bj1', '120.bx1'], 'contains': ['480.o1', '720.es1', '720.ev1', '2160.em1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [280259481600, 482676004, 88695170185, 143975, 193999455812, 80787], 'label': '77760.bo.240.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '240.cc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.cc1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 246057195
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.q1', '120.e1', '120.o1', '120.ba1', '120.bk1', '120.bv1'], 'contains': ['480.o1', '720.es1', '720.ew1', '2160.en1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [280259481600, 482676004, 143975, 193999455812, 80787, 88695348625], 'label': '77760.bo.240.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '240.cd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.cd1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246057196
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1', '80.o1', '120.bb1', '120.bo1', '120.cb1'], 'contains': ['480.p1', '720.eq1', '720.ex1', '2160.es1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [280259481600, 482676004, 88695175204, 193999420531, 80787, 179159], 'label': '77760.bo.240.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.g1', 'old_label': '240.ce1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.ce1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057197
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.p1', '120.bb1', '120.bm1'], 'contains': ['480.p1', '720.er1', '720.ey1', '2160.et1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [280259481600, 482676004, 88695353644, 193999420531, 80787, 179159], 'label': '77760.bo.240.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.s1', 'old_label': '240.cf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.cf1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057198
    {'ambient': '77760.bo', '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': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['10.a1'], 'contains': ['40.b1', '40.c1', '40.e1', '40.m1', '40.n1', '40.p1', '40.r1', '60.a1', '60.f1', '180.w1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [143975, 80787, 174400173363, 180587277504, 83543730, 93449001331, 183845, 80880, 456053074316], 'label': '77760.bo.20.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '20.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.a1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246057199
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['80.r1', '120.a1', '120.n1', '120.v1'], 'contains': ['480.r1', '480.x1', '480.bf1', '720.ez1', '720.fa1', '720.fb1', '720.fc1', '720.fd1', '720.fe1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [456053207518, 174400208787, 93449036612, 143975, 180587415845, 80787], 'label': '77760.bo.240.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '240.cg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.cg1', 'subgroup_fusion': None, 'weyl_group': '1296.3538'}
  • id: 246057200
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.bf1', '80.r1', '120.f1', '120.l1', '120.bd1'], 'contains': ['480.s1', '480.bb1', '480.be1', '720.ez1', '720.ff1', '720.fg1', '720.fh1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [143975, 80787, 375138172555, 368871230130, 80880, 174436416243], 'label': '77760.bo.240.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '240.ch1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.ch1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057201
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['80.r1', '120.g1'], 'contains': ['480.t1', '480.w1', '480.bc1', '720.fd1', '720.fg1', '720.fr1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [93449036612, 143975, 174400173363, 456053150130, 180587272349, 80787], 'label': '77760.bo.240.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.g1', 'old_label': '240.ci1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.ci1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057202
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['80.r1', '120.c1', '120.h1', '120.v1'], 'contains': ['480.u1', '480.x1', '480.bd1', '720.fe1', '720.ff1', '720.fi1', '720.fj1', '720.fr1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [93448857748, 174400173363, 456053073961, 180587450885, 80880, 80787], 'label': '77760.bo.240.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '240.cj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.cj1', 'subgroup_fusion': None, 'weyl_group': '1296.3538'}
  • id: 246057203
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.bg1', '80.r1', '120.i1', '120.l1', '120.bc1'], 'contains': ['480.v1', '480.y1', '480.be1', '720.fc1', '720.fh1', '720.fr1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [368871287518, 375138087093, 143975, 174436416243, 80880, 80787], 'label': '77760.bo.240.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '240.ck1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.ck1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057204
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['80.s1', '120.g1'], 'contains': ['480.q1', '480.t1', '480.bg1', '720.fm1', '720.fo1', '720.fq1', '720.fs1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [180587456184, 456053207518, 93449036612, 143975, 174400173363, 80787], 'label': '77760.bo.240.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.g1', 'old_label': '240.cl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.cl1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057205
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['80.s1', '120.a1', '120.h1', '120.y1'], 'contains': ['480.r1', '480.u1', '480.bh1', '720.fk1', '720.fl1', '720.fo1', '720.fp1', '720.fs1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [180587456184, 93448857748, 174400173363, 456053073961, 80880, 80787], 'label': '77760.bo.240.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '240.cm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.cm1', 'subgroup_fusion': None, 'weyl_group': '1296.3538'}
  • id: 246057206
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '240.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.bh1', '80.s1', '120.f1', '120.i1', '120.bf1'], 'contains': ['480.s1', '480.v1', '480.bi1', '720.fl1', '720.fm1', '720.fn1', '720.fs1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [143975, 174436416243, 375138270474, 80880, 80787, 368871154316], 'label': '77760.bo.240.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '240.cn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.cn1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057207
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.a1', '135.a1'], 'contains': ['540.a1', '540.f1', '540.g1', '540.fj1', '540.fq1', '540.gm1', '540.gz1', '810.d1', '810.e1', '810.f1', '1080.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [355462818505, 179012, 482849425, 462320363665, 87661007305, 85705, 375138305757], 'label': '77760.bo.270.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '270.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057208
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.b1', '135.a1'], 'contains': ['540.b1', '540.e1', '540.g1', '540.fu1', '540.fw1', '540.go1', '540.gy1', '810.b1', '810.g1', '1080.b1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [357597, 45363, 461841281758, 262496505600, 448908283914, 19679027763, 462320011466], 'label': '77760.bo.270.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '270.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.b1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057209
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '10.a1'], 'contains': ['40.b1', '40.d1', '40.m1', '40.o1', '40.q1', '60.b1', '60.g1', '180.z1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [143975, 80787, 83641651, 174400173363, 180587277504, 93449001331, 183845, 80880, 456053074316], 'label': '77760.bo.20.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '20.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.b1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246057210
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.a1', '90.c1', '135.a1'], 'contains': ['540.a1', '540.b1', '540.i1', '540.fe1', '540.fs1', '540.gb1', '540.hj1', '810.h1', '810.i1', '1080.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841090746, 462320328241, 224515, 85946, 448908283441, 19678982400, 262496730115], 'label': '77760.bo.270.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '270.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.c1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246057211
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.b1', '90.d1', '135.a1'], 'contains': ['540.e1', '540.f1', '540.i1', '540.gt1', '540.gw1', '540.hl1', '540.hn1', '810.j1', '810.k1', '1080.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [355462737961, 87661140625, 5161, 482635561, 375138092159, 224515, 462320283450], 'label': '77760.bo.270.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '270.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.d1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057212
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1', '90.e1', '90.f1'], 'contains': ['540.c1', '540.d1', '540.h1', '540.j1', '540.k1', '540.cs1', '540.ct1', '540.cx1', '2430.i1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [83462998, 598, 456053154955, 174400128000, 85946, 180587232000, 93448857600], 'label': '77760.bo.270.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.e1', 'old_label': '270.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.e1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246057213
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.g1', '135.c1'], 'contains': ['540.l1', '540.p1', '540.ba1', '540.bb1', '540.bc1', '540.en1', '540.es1', '540.et1', '540.gd1', '540.gh1', '540.gl1', '810.a1', '810.p1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [461841223825, 19679028004, 143975, 448908284158, 85805, 80787, 462320328386], 'label': '77760.bo.270.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '270.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.f1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057214
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.b1', '90.h1', '135.c1'], 'contains': ['540.o1', '540.p2', '540.q1', '540.y1', '540.ba1', '540.bj1', '540.bl1', '540.em1', '540.eo1', '540.ew1', '540.ex1', '540.gg1', '540.gi1', '540.gn1', '540.he1', '810.b1', '810.r1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841223825, 19679028004, 143975, 448908284158, 462320328958, 85805, 80787], 'label': '77760.bo.270.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '270.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.g1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057215
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.i1', '135.c1'], 'contains': ['540.n1', '540.p2', '540.r1', '540.z1', '540.bc1', '540.ej1', '540.eq1', '540.fa1', '540.fb1', '540.ge1', '540.gj1', '810.c1', '810.t1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [461841090505, 277050, 19678982548, 80880, 80787, 448908283914, 462320046985], 'label': '77760.bo.270.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '270.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.h1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057216
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.j1', '135.a1'], 'contains': ['540.v1', '540.be1', '540.bk1', '540.fe1', '540.fq1', '540.gt1', '540.gy1', '810.e1', '810.u1', '1080.n1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841143042, 224515, 462320328958, 138242, 448908283441, 19678982400, 262496730115], 'label': '77760.bo.270.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '270.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.i1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057217
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.a1', '90.l1', '135.c1'], 'contains': ['540.m1', '540.n1', '540.o1', '540.p1', '540.s1', '540.bg1', '540.bl1', '540.ei1', '540.ek1', '540.ep1', '540.er1', '540.fg1', '540.fl1', '540.gq1', '540.ha1', '810.d1', '810.v1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841090505, 277050, 19678982548, 462320328958, 80880, 80787, 448908283914], 'label': '77760.bo.270.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '270.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.j1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057218
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.a1', '90.j1', '135.b1'], 'contains': ['540.t1', '540.bh1', '540.bm1', '540.fh1', '540.fn1', '540.gr1', '540.hb1', '810.e1', '810.v1', '1080.p1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841090505, 19679028004, 5309, 448908284158, 462320046842, 262496586387, 80787], 'label': '77760.bo.270.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '270.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.k1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057219
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.a1', '90.k1'], 'contains': ['540.u1', '540.bi1', '540.bn1', '540.fi1', '540.fo1', '540.gs1', '540.hc1', '810.f1', '810.v1', '1080.q1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [183845, 355462871189, 462320225425, 87661059842, 482635561, 375138270245, 80787], 'label': '77760.bo.270.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.l1', 'old_label': '270.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.l1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057220
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '10.a1'], 'contains': ['40.c1', '40.d1', '40.p1', '40.q1', '40.s1', '60.c1', '60.k1', '180.bh1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [180587277504, 456053074316, 93449001331, 83543730, 143975, 174400173363, 85805, 80880, 80787], 'label': '77760.bo.20.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '20.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.c1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246057221
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.m1', '135.a1'], 'contains': ['540.x1', '540.bd1', '540.bk1', '540.fs1', '540.fw1', '540.gw1', '540.gz1', '810.g1', '810.q1', '1080.s1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [355462818505, 87661105201, 462320225425, 40585, 482768881, 375138305425, 80880], 'label': '77760.bo.270.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '270.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.m1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057222
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.b1', '90.m1', '135.b1'], 'contains': ['540.w1', '540.bf1', '540.bm1', '540.ft1', '540.fv1', '540.gu1', '540.hb1', '810.g1', '810.r1', '1080.t1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [277050, 461841327358, 19679028004, 448908284158, 262496586387, 80787, 462320046985], 'label': '77760.bo.270.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '270.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.n1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057223
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.ce2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.c1', '90.n1', '135.c1'], 'contains': ['540.l1', '540.q1', '540.r1', '540.s1', '540.bo1', '540.el1', '540.ev1', '540.ez1', '540.fd1', '540.fy1', '540.hf1', '810.h1', '810.w1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [277050, 19678982548, 461841281758, 462320328958, 80880, 80787, 448908283914], 'label': '77760.bo.270.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '270.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.o1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246057224
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.c1', '90.c1', '90.o1', '135.b1'], 'contains': ['540.t1', '540.w1', '540.bp1', '540.fh1', '540.ft1', '540.ga1', '540.hk1', '810.i1', '810.w1', '1080.u1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841009961, 40349, 19679028004, 448908001949, 262496586387, 80787, 462320046749], 'label': '77760.bo.270.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '270.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.p1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057225
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.d1', '90.o1', '135.a1'], 'contains': ['540.v1', '540.x1', '540.bq1', '540.fj1', '540.fu1', '540.gb1', '540.hl1', '810.i1', '810.x1', '1080.v1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [355462951825, 87661140625, 482849425, 219025, 375138127292, 143975, 462320328958], 'label': '77760.bo.270.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '270.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.q1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057226
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.d1', '90.p1', '135.c1'], 'contains': ['540.z1', '540.bb1', '540.bg1', '540.bj1', '540.bo1', '540.gf1', '540.gk1', '540.gv1', '540.hd1', '540.hg1', '540.hh1', '810.j1', '810.z1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [183845, 448908001949, 19678982548, 461841188401, 80880, 80787, 462320046985], 'label': '77760.bo.270.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '270.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.r1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057227
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.e1', '90.q1', '135.a1'], 'contains': ['540.bd1', '540.be1', '540.bq1', '540.gm1', '540.go1', '540.hj1', '540.hn1', '810.k1', '810.y1', '1080.bc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87661244013, 462320283450, 355462773242, 85805, 482635561, 375138363450, 45363], 'label': '77760.bo.270.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '270.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.s1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057228
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.f1', '90.d1', '90.q1', '135.b1'], 'contains': ['540.bf1', '540.bh1', '540.bp1', '540.gr1', '540.gu1', '540.hk1', '540.hm1', '810.k1', '810.z1', '1080.bd1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841090505, 19679028004, 5309, 448908284158, 462320328958, 262496586387, 80787], 'label': '77760.bo.270.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '270.t1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.t1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057229
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.r1', '135.a1'], 'contains': ['540.a1', '540.e1', '540.v1', '540.bd1', '540.bs1', '540.dl1', '540.dw1', '810.l1', '810.bd1', '1080.bi1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [462320092205, 461841090505, 262496506293, 19678982548, 85805, 148, 693], 'label': '77760.bo.270.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '270.u1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.u1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057230
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['54.d1', '90.s1', '135.a1'], 'contains': ['540.b1', '540.f1', '540.x1', '540.be1', '540.bs1', '540.dp1', '540.dy1', '810.m1', '810.bb1', '1080.bj1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [188331269880, 482849285, 87182103845, 85805, 375138172205, 80880, 143304], 'label': '77760.bo.270.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '270.v1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.v1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057231
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '20.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['10.a1'], 'contains': ['40.a1', '40.b1', '40.c1', '40.f1', '40.g1', '40.h1', '40.i1', '40.j1', '60.m1', '60.o1'], 'core': '720.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [180587277504, 93449001331, 83543730, 143975, 174400173363, 85805, 80880, 80787, 143304], 'label': '77760.bo.20.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '20.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.d1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246057232
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.g1', '90.t1', '135.a1'], 'contains': ['540.g1', '540.i1', '540.bk1', '540.bq1', '540.bs1', '540.ec1', '540.eg1', '810.n1', '810.be1', '1080.bk1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [5161, 19203891571, 224184, 374659361850, 224515, 87657516984, 87182197050], 'label': '77760.bo.270.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '270.w1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.w1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057233
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.r1', '135.b1'], 'contains': ['540.t1', '540.bf1', '540.bu1', '540.cq1', '540.cu1', '810.l1', '810.bi1', '1080.bl1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [461841045385, 19679028004, 85805, 80787, 262496586694, 462320046985, 693], 'label': '77760.bo.270.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '270.x1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.x1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057234
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.e1', '90.s1', '135.b1'], 'contains': ['540.w1', '540.bh1', '540.bu1', '540.cr1', '540.cv1', '810.m1', '810.bg1', '1080.bm1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [443120071204, 442641024000, 180667203842, 442162022400, 85805, 80787, 143304], 'label': '77760.bo.270.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '270.y1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.y1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057235
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.h1', '90.t1', '135.b1'], 'contains': ['540.bm1', '540.bp1', '540.bu1', '540.cw1', '540.cy1', '810.n1', '810.bj1', '1080.bn1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [80787, 87182058242, 19203833784, 224184, 87657516984, 374659268645, 40349], 'label': '77760.bo.270.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '270.z1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.z1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057236
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.g1', '135.c1'], 'contains': ['540.bv1', '540.bz1', '540.cf1', '540.cg1', '540.ch1', '540.ei1', '540.el1', '540.et1', '540.gf1', '540.gg1', '540.gj1', '810.o1', '810.p1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [80787, 461841281758, 85805, 19678982548, 448908283914, 80880, 462320046985], 'label': '77760.bo.270.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '270.ba1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.ba1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057237
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.h1', '90.m1', '135.c1'], 'contains': ['540.by1', '540.bz2', '540.ca1', '540.cd1', '540.cf1', '540.cj1', '540.ck1', '540.ej1', '540.ek1', '540.ev1', '540.ex1', '540.gh1', '540.gi1', '540.gv1', '540.ha1', '810.q1', '810.r1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [80787, 461841281758, 85805, 462320328958, 19678982548, 448908283914, 80880], 'label': '77760.bo.270.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '270.bb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.bb1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057238
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.i1', '135.c1'], 'contains': ['540.bx1', '540.bz2', '540.cb1', '540.ce1', '540.ch1', '540.em1', '540.ep1', '540.ez1', '540.fb1', '540.gk1', '540.gl1', '810.s1', '810.t1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [183845, 461841090505, 19679028004, 143975, 448908284158, 462320328485, 80787], 'label': '77760.bo.270.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '270.bc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.bc1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057239
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.j1', '90.k1', '90.l1', '135.c1'], 'contains': ['540.bw1', '540.bx1', '540.by1', '540.bz1', '540.cc1', '540.ci1', '540.ck1', '540.en1', '540.eo1', '540.eq1', '540.er1', '540.fd1', '540.fl1', '540.hd1', '540.he1', '810.u1', '810.v1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841223825, 183845, 448908283441, 19679028004, 143975, 462320328958, 80787], 'label': '77760.bo.270.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '270.bd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.bd1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057240
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.n1', '90.o1', '135.c1'], 'contains': ['540.bv1', '540.ca1', '540.cb1', '540.cc1', '540.cl1', '540.es1', '540.ew1', '540.fa1', '540.fg1', '540.fy1', '540.hg1', '810.w1', '810.x1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [461841223825, 183845, 19679028004, 143975, 448908284158, 462320328958, 80787], 'label': '77760.bo.270.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '270.be1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.be1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057241
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.p1', '90.q1', '135.c1'], 'contains': ['540.ce1', '540.cg1', '540.ci1', '540.cj1', '540.cl1', '540.gd1', '540.ge1', '540.gn1', '540.gq1', '540.hf1', '540.hh1', '810.y1', '810.z1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [461841223825, 183845, 448908283441, 19679028004, 143975, 80787, 462320328241], 'label': '77760.bo.270.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '270.bf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.bf1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057242
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '2.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': ['38880.c1', '38880.f1', '38880.a1', '38880.g1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.d1', '6.i1', '12.k1', '20.h1', '30.l1'], 'core': '2.e1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [93924311494, 143975, 80880, 80787, 462320328386, 143304], 'label': '77760.bo.2.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.d1'], 'normalizer': '1.a1', 'old_label': '2.e1', 'projective_image': '77760.bo', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1', 'subgroup_fusion': None, 'weyl_group': '77760.bo'}
  • id: 246057243
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '20.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '10.a1'], 'contains': ['40.d1', '40.e1', '40.g1', '40.k1', '40.l1', '60.n1', '180.bx1'], 'core': '720.a1', 'coset_action_label': None, 'count': 10, 'diagramx': None, 'generators': [143975, 80787, 482768881, 143304, 280259521949, 88695348625, 85805, 80880, 193999357894], 'label': '77760.bo.20.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '20.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.e1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246057244
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.u1', '135.c1'], 'contains': ['540.l1', '540.m1', '540.y1', '540.z1', '540.bv1', '540.bw1', '540.cd1', '540.ce1', '540.cm2', '540.cn1', '540.co1', '540.dc1', '540.dd1', '540.ds1', '540.dt1', '810.ba1', '810.bf1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [7185162389, 19678982548, 85805, 80880, 80787, 462320046985, 143304], 'label': '77760.bo.270.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '270.bg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.bg1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057245
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.s1', '90.v1', '135.c1'], 'contains': ['540.n1', '540.q1', '540.ba1', '540.bg1', '540.bx1', '540.ca1', '540.cf1', '540.ci1', '540.cm1', '540.cn1', '540.cp1', '540.db1', '540.df1', '540.dr1', '540.dx1', '810.bb1', '810.bg1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87182277597, 482849425, 143975, 375138270474, 85805, 80787, 143304], 'label': '77760.bo.270.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '270.bh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.bh1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057246
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['30.e1', '90.w1', '135.c1'], 'contains': ['540.o1', '540.r1', '540.bb1', '540.by1', '540.cb1', '540.cg1', '540.cm1', '540.co1', '540.da1', '540.dh1', '540.du1', '810.bc1', '810.bh1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [87261834480, 456053074316, 83543730, 85805, 80880, 80787, 693], 'label': '77760.bo.270.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '270.bi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.bi1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057247
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.r1', '90.x1', '135.c1'], 'contains': ['540.p1', '540.p2', '540.s1', '540.bj1', '540.bz1', '540.bz2', '540.cc1', '540.cj1', '540.cm1', '540.cm2', '540.cp1', '540.cz1', '540.cz2', '540.dj1', '540.ea1', '810.bd1', '810.bi1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841090505, 143975, 178680, 80787, 462320328485, 19679028004, 5309], 'label': '77760.bo.270.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '270.bj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.bj1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057248
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.t1', '90.y1', '135.c1'], 'contains': ['540.bc1', '540.bl1', '540.bo1', '540.ch1', '540.ck1', '540.cl1', '540.co1', '540.cp1', '540.dv1', '540.eb1', '540.ee1', '810.be1', '810.bj1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [87182277597, 178680, 5309, 143975, 374659361850, 355938110909, 80787], 'label': '77760.bo.270.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '270.bk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.bk1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057249
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.z1', '135.b1'], 'contains': ['540.cq1', '540.cv1', '540.cw1', '540.fh1', '540.gu1', '810.bn1', '810.bo1', '810.bp1', '1080.bz1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [482849425, 178680, 355462911480, 462320052004, 87661145547, 80787, 375138086400], 'label': '77760.bo.270.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '270.bl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.bl1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057250
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.ba1', '135.b1'], 'contains': ['540.cr1', '540.cu1', '540.cw1', '540.ft1', '540.gr1', '810.bl1', '810.bq1', '1080.ca1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [482849425, 178680, 355462911480, 87661059842, 462320046842, 80787, 375138126842], 'label': '77760.bo.270.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '270.bm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.bm1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057251
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.j1', '90.bb1', '90.bc1', '135.b1'], 'contains': ['540.cq1', '540.cr1', '540.cy1', '540.fn1', '540.fv1', '540.ga1', '540.hm1', '810.br1', '810.bs1', '1080.cd1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [317399, 448908278999, 19679028004, 462320052004, 461841050404, 80787, 262496822999], 'label': '77760.bo.270.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '270.bn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.bn1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246057252
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.k1', '90.bd1', '135.b1'], 'contains': ['540.cu1', '540.cv1', '540.cy1', '540.hb1', '540.hk1', '810.bt1', '810.bu1', '1080.cf1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [482808988, 375138091561, 224184, 87661059842, 80787, 355462956984, 462320046749], 'label': '77760.bo.270.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '270.bo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.bo1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057253
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.be1', '135.c1'], 'contains': ['540.cz1', '540.dc1', '540.dr1', '540.du1', '540.dv1', '540.el1', '540.er1', '540.es1', '540.ge1', '540.gi1', '540.gk1', '810.bk1', '810.bv1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [362615, 461841090505, 462320052004, 19678982548, 80880, 80787, 448908283914], 'label': '77760.bo.270.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '270.bp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.bp1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057254
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '20.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['10.a1'], 'contains': ['40.i1', '40.j1', '40.l1', '40.m1', '40.p1', '60.q1', '180.cq1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [180587277504, 456053074316, 93449001331, 83543730, 143975, 174400173363, 80880, 80787, 143304], 'label': '77760.bo.20.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '20.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.f1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246057255
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.ba1', '90.bf1', '135.c1'], 'contains': ['540.cz2', '540.da1', '540.df1', '540.dr1', '540.ds1', '540.ea1', '540.eb1', '540.ep1', '540.eq1', '540.ev1', '540.ew1', '540.gg1', '540.gh1', '540.gq1', '540.hd1', '810.bl1', '810.bw1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [448908278999, 224184, 19679028004, 143975, 461841050404, 80787, 462320328241], 'label': '77760.bo.270.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '270.bq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.bq1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057256
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.bg1', '135.c1'], 'contains': ['540.cz2', '540.db1', '540.dh1', '540.dt1', '540.dv1', '540.ek1', '540.eo1', '540.ez1', '540.fa1', '540.gd1', '540.gf1', '810.bm1', '810.bx1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [448908278999, 362615, 461841090505, 19678982548, 80880, 80787, 462320046985], 'label': '77760.bo.270.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '270.br1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.br1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057275
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['54.b1', '108.c1', '108.g1', '108.h1', '162.a1'], 'contains': ['648.c1', '648.q1', '648.r1', '1620.s1', '1944.b1', '3240.m1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [174879492215, 322558, 462320046985], 'label': '77760.bo.324.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '324.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.b1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
  • id: 246057257
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.z1', '90.bh1', '135.c1'], 'contains': ['540.cz1', '540.da1', '540.db1', '540.dd1', '540.dj1', '540.dx1', '540.eb1', '540.ei1', '540.ej1', '540.em1', '540.en1', '540.fd1', '540.fg1', '540.gn1', '540.gv1', '810.bn1', '810.by1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [448908278999, 461841009961, 224184, 462320323320, 19679028004, 143975, 80787], 'label': '77760.bo.270.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '270.bs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.bs1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057258
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.z1', '135.a1'], 'contains': ['540.dl1', '540.dy1', '540.ec1', '540.fe1', '540.fj1', '540.go1', '540.gw1', '810.bo1', '810.by1', '1080.cl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [355462911480, 87661100280, 482768881, 462320006400, 80880, 375138086400, 143304], 'label': '77760.bo.270.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '270.bt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.bt1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057259
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.z1'], 'contains': ['540.dm1', '540.dz1', '540.ed1', '540.ff1', '540.fk1', '540.gp1', '540.gx1', '810.bp1', '810.by1', '1080.cm1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [87661100280, 355462956747, 482768881, 462320006400, 80880, 375138086400, 143304], 'label': '77760.bo.270.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bu1', 'old_label': '270.bu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.bu1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057260
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.ba1', '135.a1'], 'contains': ['540.dp1', '540.dw1', '540.ec1', '540.fs1', '540.fu1', '540.gm1', '540.gt1', '810.bq1', '810.bw1', '1080.cp1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87661105201, 355462911480, 375138126985, 482768881, 80880, 462320046985, 143304], 'label': '77760.bo.270.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '270.bv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.bv1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057261
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.bb1', '90.bi1', '135.c1'], 'contains': ['540.dc1', '540.df1', '540.dh1', '540.dj1', '540.ee1', '540.et1', '540.ex1', '540.fb1', '540.fl1', '540.fy1', '540.hh1', '810.br1', '810.bz1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [448908278999, 224184, 462320323320, 19679028004, 143975, 461841050404, 80787], 'label': '77760.bo.270.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '270.bw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.bw1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246057262
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.bc1', '90.bi1'], 'contains': ['540.de1', '540.dg1', '540.di1', '540.dk1', '540.ef1', '540.eu1', '540.ey1', '540.fc1', '540.fm1', '540.fz1', '540.hi1', '810.br1', '810.ca1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [448908278999, 462320323467, 19679028004, 461841050404, 80787, 143304, 179159], 'label': '77760.bo.270.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '270.bx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.bx1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246057263
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.l1', '90.bb1', '135.a1'], 'contains': ['540.dl1', '540.dp1', '540.eg1', '540.fq1', '540.fw1', '540.gb1', '540.hn1', '810.bs1', '810.bz1', '1080.cq1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [262496868215, 461841050163, 362615, 45363, 448908243571, 462320006400, 19679027763], 'label': '77760.bo.270.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '270.by1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.by1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057264
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.m1', '90.bc1'], 'contains': ['540.dn1', '540.dq1', '540.eh1', '540.fr1', '540.fx1', '540.gc1', '540.ho1', '810.bs1', '810.ca1', '1080.cr1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [355462956984, 375138311012, 482854584, 224184, 462320323467, 224612, 87661145784], 'label': '77760.bo.270.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '270.bz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.bz1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057265
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '20.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1', '10.a1'], 'contains': ['40.i1', '40.k1', '40.n1', '40.o1', '40.s1', '60.r1', '60.s1', '180.cv1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 10, 'diagramx': None, 'generators': [180587277504, 93449001331, 83543730, 143975, 174400173363, 456053150130, 80880, 80787, 143304], 'label': '77760.bo.20.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '20.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.g1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246057266
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['90.bd1', '90.bj1', '135.c1'], 'contains': ['540.dt1', '540.du1', '540.dx1', '540.ea1', '540.ee1', '540.gj1', '540.gl1', '540.ha1', '540.he1', '540.hf1', '540.hg1', '810.bt1', '810.cb1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [362615, 461841004948, 19678982548, 80880, 80787, 448908283914, 462320046985], 'label': '77760.bo.270.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '270.ca1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.ca1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057267
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '270.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.n1', '90.bd1', '135.a1'], 'contains': ['540.dw1', '540.dy1', '540.eg1', '540.gy1', '540.gz1', '540.hj1', '540.hl1', '810.bu1', '810.cb1', '1080.da1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87661105201, 482854584, 355462911480, 375138126985, 80880, 462320046985, 143304], 'label': '77760.bo.270.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '270.cb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.cb1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057268
    {'ambient': '77760.bo', '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': '15552.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.a1', '144.b1', '144.c1'], 'contains': ['576.a1', '864.a1', '864.b1', '1440.a1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [18764743922, 183845, 143975, 80880, 80787], 'label': '77760.bo.288.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '288.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.a1', 'subgroup_fusion': None, 'weyl_group': '432.300'}
  • id: 246057269
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '288.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1', '144.d1', '144.e1'], 'contains': ['576.a1', '864.c1', '864.d1', '1440.b1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18764748747, 143975, 80880, 80787, 143304], 'label': '77760.bo.288.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '288.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.b1', 'subgroup_fusion': None, 'weyl_group': '144.143'}
  • id: 246057270
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '288.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1', '144.a1', '144.d1', '144.f1', '144.g1', '144.h1'], 'contains': ['576.a1', '864.e1', '864.f1', '1440.be1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1037836800, 143975, 18764570163, 80880, 80787], 'label': '77760.bo.288.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '288.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.c1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 246057271
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '288.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.a1', '144.b1', '144.e1'], 'contains': ['576.a1', '864.g1', '864.h1', '1440.cp1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [143975, 1038020645, 18764570163, 80880, 80787], 'label': '77760.bo.288.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '288.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.d1', 'subgroup_fusion': None, 'weyl_group': '2160.cr'}
  • id: 246057272
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '288.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1', '144.d1'], 'contains': ['576.a1', '864.i1', '864.j1', '1440.cz1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1037980104, 143975, 18764570163, 80880, 80787], 'label': '77760.bo.288.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '288.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.e1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 246057273
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '320.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.a1', '160.b1', '160.c1', '160.d1', '160.e1', '160.f1', '160.g1', '160.h1'], 'contains': ['960.a1', '960.b1', '960.c1', '960.d1', '960.e1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 10, 'diagramx': None, 'generators': [143975, 193999455812, 280259527104, 80880, 80787], 'label': '77760.bo.320.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '320.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '320.a1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 246057274
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '324.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.w1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['54.a1', '108.b1', '108.e1', '108.f1', '162.a1'], 'contains': ['648.c1', '648.p1', '648.q1', '1620.k1', '1944.a1', '3240.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [357597, 443555839197, 479001600], 'label': '77760.bo.324.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1', 'old_label': '324.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.a1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
  • id: 246057276
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '20.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1', '10.a1'], 'contains': ['40.j1', '40.k1', '40.q1', '40.r1', '60.t1', '180.da1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 10, 'diagramx': None, 'generators': [180587277504, 456053074316, 93449001331, 83467916, 143975, 174400173363, 80880, 80787, 143304], 'label': '77760.bo.20.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '20.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.h1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246057277
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.c1', '108.i1', '108.j1', '162.a1'], 'contains': ['648.c1', '648.l1', '1620.bb1', '1944.c1', '3240.s1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [455574067893, 349232169355, 85805, 693], 'label': '77760.bo.324.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '324.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.c1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
  • id: 246057278
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '324.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.d1', '108.k1'], 'contains': ['648.a1', '648.b1', '648.f1', '648.g1', '648.h1', '648.m1', '648.n1', '972.a1', '1620.cl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [85805, 181146153355, 269202614155, 693, 148, 267841814255], 'label': '77760.bo.324.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d1', 'old_label': '324.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.d1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246057279
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '324.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.e1', '108.k1'], 'contains': ['648.d1', '648.e1', '648.i1', '648.j1', '648.k1', '972.a1', '1620.cp1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [267841768892, 85805, 269202533759, 80787, 181146153355, 693], 'label': '77760.bo.324.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.e1', 'old_label': '324.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.e1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246057280
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '324.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.f1', '108.l1', '108.o1', '108.p1', '162.a1'], 'contains': ['648.l1', '648.p1', '648.r1', '1620.dc1', '1944.d1', '3240.bu1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [281971, 174879411571, 462320006400], 'label': '77760.bo.324.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '324.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.f1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
  • id: 246057281
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '324.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.g1', '108.m1', '108.q1', '162.a1'], 'contains': ['648.l1', '648.q1', '1620.dk1', '1944.e1', '3240.cb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [362615, 174879452158, 462320046985], 'label': '77760.bo.324.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '324.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.g1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
  • id: 246057282
    {'ambient': '77760.bo', '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': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.a1', '180.p1'], 'contains': ['720.b1', '720.d1', '720.e1', '720.de1', '720.dk1', '720.fb1', '720.fk1', '1080.a1', '1080.b1', '1080.c1', '1080.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [180587456184, 93449082115, 40349, 174400128000, 224515, 83686915], 'label': '77760.bo.360.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '360.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057283
    {'ambient': '77760.bo', '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': '12960.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.b1', '180.a1', '180.b1', '180.p1'], 'contains': ['720.b1', '720.c1', '720.cz1', '720.dp1', '720.ek1', '1080.e1', '1080.f1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [456053074316, 180587232243, 93448857748, 148, 174400128148, 5759], 'label': '77760.bo.360.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '360.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.b1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246057284
    {'ambient': '77760.bo', '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': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.c1', '180.a1', '180.c1', '180.p1'], 'contains': ['720.c1', '720.d1', '720.em1', '720.eo1', '720.fj1', '1080.g1', '1080.i1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [180587277504, 219025, 174400208880, 456053073961, 93448938480, 80880], 'label': '77760.bo.360.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '360.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.c1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057285
    {'ambient': '77760.bo', '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': '12960.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.b1', '120.d1', '180.b1', '180.c1', '180.q1'], 'contains': ['720.c1', '720.et1', '720.ev1', '1080.j1', '3240.i1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [88695170185, 143975, 40585, 280259522185, 193999420775, 482670985], 'label': '77760.bo.360.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '360.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.d1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246057286
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.e1', '180.a1', '180.q1'], 'contains': ['720.c1', '720.eu1', '720.ew1', '1080.k1', '3240.j1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [219025, 88695170185, 280259620081, 193999276800, 482768881, 80880], 'label': '77760.bo.360.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '360.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.e1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057287
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.a1', 'complements': ['3240.bl1', '3240.t2', '3240.cf2', '3240.a2', '3240.cs2', '3240.cs1', '3240.cf1', '3240.cs3', '3240.t1', '3240.cs4', '3240.a1', '3240.c1'], 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '12.a1', '12.b1', '12.c1', '12.d1', '12.h1', '12.m1', '12.n1'], 'contains': ['72.a1', '72.q1', '144.i1', '240.ca1', '360.gg1'], 'core': '24.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [274511507904, 80880, 80787, 87182000787], 'label': '77760.bo.24.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': ['8.a1', '12.a1', '12.b1', '12.c1'], 'normal_contains': ['72.a1', '8640.a1'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '77760.bo', 'quotient_action_image': '8.5', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '8640.t'}
  • id: 246057288
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.a1', '120.a1', '120.f1', '180.bt1'], 'contains': ['720.f1', '720.r1', '720.t1', '720.cq1', '720.cr1', '720.ez1', '720.fs1', '1080.a1', '1080.o1', '1080.p1', '1080.q1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [442641386187, 40349, 143975, 997965813, 519235320, 80787], 'label': '77760.bo.360.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '360.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.f1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057289
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.h1', '180.p1'], 'contains': ['720.j1', '720.n1', '720.s1', '720.cz1', '720.dk1', '720.fj1', '720.fk1', '1080.d1', '1080.n1', '1080.s1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [180587456184, 174400208880, 40585, 456053073961, 93448938480, 80880], 'label': '77760.bo.360.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '360.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.g1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057290
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.b1', '120.a1', '120.i1', '180.bt1'], 'contains': ['720.g1', '720.o1', '720.t1', '720.da1', '720.df1', '720.fc1', '720.fl1', '1080.b1', '1080.o1', '1080.t1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [442641386755, 998099012, 5309, 143975, 519235320, 80787], 'label': '77760.bo.360.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '360.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.h1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057291
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.a1', '120.g1'], 'contains': ['720.h1', '720.p1', '720.u1', '720.db1', '720.dh1', '720.fd1', '720.fo1', '1080.c1', '1080.q1', '1080.t1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [180587456184, 183845, 93448938387, 174400173363, 456053073961, 80787], 'label': '77760.bo.360.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.i1', 'old_label': '360.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.i1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057292
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.a1', '120.h1', '180.r1'], 'contains': ['720.i1', '720.q1', '720.v1', '720.dc1', '720.dj1', '720.fe1', '720.fp1', '1080.d1', '1080.p1', '1080.t1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [180587456184, 183845, 174400208787, 93448938387, 456053073961, 80787], 'label': '77760.bo.360.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.r1', 'old_label': '360.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.j1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057293
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.c1', '90.c1', '120.b1', '120.j1', '180.bt1'], 'contains': ['720.f1', '720.g1', '720.k1', '720.cn1', '720.cx1', '720.dm1', '720.eb1', '1080.e1', '1080.r1', '1080.u1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [442641386187, 998099012, 143975, 519235320, 85805, 80787], 'label': '77760.bo.360.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '360.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.k1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057331
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.d1', '12.e1', '12.f1', '12.k1'], 'contains': ['48.a1', '72.m1', '72.n1', '120.bq1', '144.g1', '240.bt1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [174879406797, 143975, 462320328958, 80880, 80787], 'label': '77760.bo.24.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1', 'subgroup_fusion': None, 'weyl_group': '12960.bv'}
  • id: 246057294
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.b1', '120.k1', '180.g1', '180.h1', '180.r1'], 'contains': ['720.i1', '720.l1', '720.dc1', '720.do1', '720.el1', '1080.f1', '1080.u1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [183845, 174400208787, 93448938387, 83462400, 180587232000, 80787], 'label': '77760.bo.360.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '360.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.l1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057295
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.k1', '180.f1', '180.i1', '180.p1'], 'contains': ['720.j1', '720.m1', '720.de1', '720.dp1', '720.em1', '1080.f1', '1080.v1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [174400128000, 143975, 180587232000, 456053154955, 93449001575, 183845], 'label': '77760.bo.360.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '360.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.m1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057296
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.d1', '90.d1', '120.c1', '120.l1', '180.bt1'], 'contains': ['720.k1', '720.o1', '720.r1', '720.ec1', '720.ed1', '720.ff1', '720.fr1', '1080.g1', '1080.w1', '1080.bd1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [40349, 442641386852, 143975, 997965813, 519235320, 80787], 'label': '77760.bo.360.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '360.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.n1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057297
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.b1', '120.m1', '180.d1', '180.e1', '180.j1', '180.k1', '180.l1', '180.o1', '180.bu1'], 'contains': ['720.ef1', '1080.h1', '1080.be1', '1080.bf1', '1080.bg1', '1440.d1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [183845, 268244570163, 194518275844, 80880, 80787, 274467916948], 'label': '77760.bo.360.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '360.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.o1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246057298
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.a1', '12.e1', '12.f1', '12.g1'], 'contains': ['48.a1', '72.b1', '72.e1', '120.m1', '144.a1', '240.i1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25470588092, 183845, 143975, 80880, 80787, 286482914492], 'label': '77760.bo.24.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1', 'subgroup_fusion': None, 'weyl_group': '12960.bv'}
  • id: 246057299
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.n1', '180.f1', '180.m1', '180.p1'], 'contains': ['720.m1', '720.n1', '720.ek1', '720.eo1', '720.fb1', '1080.i1', '1080.bc1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [93448857748, 174400128148, 180587232243, 5066, 456053074316, 148], 'label': '77760.bo.360.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '360.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.p1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057300
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.c1', '120.n1', '180.g1', '180.n1', '180.r1'], 'contains': ['720.l1', '720.q1', '720.el1', '720.en1', '720.fe1', '1080.i1', '1080.bd1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [183845, 174400208787, 93448938387, 456053073961, 180587232000, 80787], 'label': '77760.bo.360.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '360.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.q1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057301
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.e1', '120.d1', '120.o1', '180.h1', '180.n1', '180.s1'], 'contains': ['720.l1', '720.eq1', '720.es1', '1080.j1', '3240.ba1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [183845, 482849425, 280259665445, 80787, 88695348625, 193999357587], 'label': '77760.bo.360.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '360.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.r1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057302
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.e1', '120.p1', '180.g1', '180.s1'], 'contains': ['720.l1', '720.er1', '720.es1', '1080.k1', '3240.bb1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [183845, 482849425, 88695170185, 280259665445, 80787, 193999357587], 'label': '77760.bo.360.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '360.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.s1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057303
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.f1', '120.o1', '180.i1', '180.m1', '180.q1'], 'contains': ['720.m1', '720.et1', '720.ew1', '1080.j1', '3240.be1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [88695170185, 280259486761, 482635561, 193999276800, 40585, 80880], 'label': '77760.bo.360.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '360.t1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.t1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057304
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.p1', '180.f1', '180.q1'], 'contains': ['720.m1', '720.eu1', '720.ev1', '1080.k1', '3240.bf1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [280259486761, 482635561, 193999276800, 40585, 80880, 88695348625], 'label': '77760.bo.360.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '360.u1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.u1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057305
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.q1', '180.p1'], 'contains': ['720.b1', '720.d1', '720.j1', '720.n1', '720.w1', '720.bv1', '720.ce1', '1080.l1', '1080.bi1', '1080.bj1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [93449082115, 40349, 224184, 83462998, 174400128000, 224515], 'label': '77760.bo.360.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '360.v1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.v1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057306
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.r1', '180.p1', '180.q1'], 'contains': ['720.c1', '720.e1', '720.m1', '720.s1', '720.w1', '720.ca1', '720.ci1', '1080.m1', '1080.bk1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [482849425, 143975, 193999277493, 40585, 280259522185, 143304], 'label': '77760.bo.360.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '360.w1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.w1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057307
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.q1', '180.r1'], 'contains': ['720.i1', '720.q1', '720.x1', '720.bm1', '720.bo1', '1080.l1', '1080.bl1', '1080.bm1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [174400208787, 93448938387, 456053154955, 85805, 80787, 693], 'label': '77760.bo.360.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.r1', 'old_label': '360.x1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.x1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057308
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.r1', '180.r1', '180.s1'], 'contains': ['720.l1', '720.v1', '720.x1', '720.bn1', '720.bp1', '1080.m1', '1080.bn1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [482849425, 280259567405, 193999455627, 85805, 80787, 143304], 'label': '77760.bo.360.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '360.y1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.y1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057309
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '12.g1', '12.j1', '12.k1'], 'contains': ['48.a1', '72.g1', '72.h1', '120.bg1', '144.d1', '240.bb1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [286483098115, 143975, 80880, 80787, 25470771715, 143304], 'label': '77760.bo.24.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1', 'subgroup_fusion': None, 'weyl_group': '4320.bp'}
  • id: 246057310
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.j1', '120.f1', '120.h1', '180.bt1'], 'contains': ['720.y1', '720.bf1', '720.bi1', '720.cn1', '720.cr1', '720.ff1', '720.fl1', '1080.n1', '1080.p1', '1080.bo1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [518964004, 442641024148, 997965813, 85805, 80880, 80787], 'label': '77760.bo.360.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '360.z1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.z1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057311
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.k1', '120.f1', '120.g1'], 'contains': ['720.z1', '720.bg1', '720.bj1', '720.co1', '720.cs1', '720.fg1', '720.fm1', '1080.q1', '1080.bo1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [174436600173, 85805, 375138172205, 80880, 80787, 368871154316], 'label': '77760.bo.360.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ba1', 'old_label': '360.ba1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ba1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246057312
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.f1', '120.i1', '180.x1', '180.x2', '180.bv1'], 'contains': ['720.ba1', '720.bh1', '720.bk1', '720.cp1', '720.ct1', '720.fh1', '720.fn1', '1080.o1', '1080.bo1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [442641386424, 143975, 443120071554, 85805, 80880, 80787], 'label': '77760.bo.360.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.x1', 'old_label': '360.bb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bb1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246057313
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.bb2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.x1', '180.x2', '180.bv2'], 'contains': ['720.ba1', '720.bh1', '720.bk1', '720.cp2', '720.ct2', '720.fh2', '720.fn2', '1080.o2', '1080.bo2'], 'core': '1440.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [442641386424, 143975, 85805, 80880, 80787, 448908283914], 'label': '77760.bo.360.bb2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.bb2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bb2', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246057314
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.j1', '180.v1', '180.w1', '180.x2', '180.y1', '180.z1', '180.bc1', '180.bv1'], 'contains': ['720.ba1', '720.bc1', '720.cp1', '720.cw1', '720.dr1', '1080.r1', '1080.bp1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [87182277125, 143975, 375138270474, 85805, 80880, 80787], 'label': '77760.bo.360.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.bc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bc1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057315
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.bc2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.t1', '180.u1', '180.x1', '180.bc1', '180.bv2'], 'contains': ['720.ba1', '720.bc1', '720.cp2', '720.cw2', '720.dr2', '1080.r2', '1080.bp2'], 'core': '1440.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [448908283441, 442641386424, 143975, 85805, 80880, 80787], 'label': '77760.bo.360.bc2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.bc2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bc2', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246057316
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.m1', '120.g1', '120.h1', '120.i1', '180.bt1'], 'contains': ['720.bb1', '720.be1', '720.bi1', '720.cx1', '720.df1', '720.fr1', '720.fs1', '1080.s1', '1080.t1', '1080.bo1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [518964004, 997965504, 442641386755, 85805, 80880, 80787], 'label': '77760.bo.360.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '360.bd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bd1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057317
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.g1', '90.o1', '120.j1', '120.k1', '180.bt1'], 'contains': ['720.y1', '720.bb1', '720.bd1', '720.cq1', '720.da1', '720.dm1', '720.ec1', '1080.u1', '1080.v1', '1080.bp1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [183845, 174436554242, 368871234955, 143975, 375138172555, 80787], 'label': '77760.bo.360.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '360.be1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.be1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057318
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.l1', '180.w1', '180.x1', '180.bg1', '180.bh1', '180.bm1', '180.bn1', '180.bv1'], 'contains': ['720.bc1', '720.bh1', '720.dr1', '720.ds1', '720.fh1', '1080.w1', '1080.bq1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [183845, 442641386755, 443120250115, 143975, 80880, 80787], 'label': '77760.bo.360.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.bf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bf1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057319
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.bf2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.x2', '180.be1', '180.bf1', '180.bn1', '180.bv2'], 'contains': ['720.bc1', '720.bh1', '720.dr2', '720.ds2', '720.fh2', '1080.w2', '1080.bq2'], 'core': '1440.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [442641386755, 143975, 85805, 80880, 80787, 448908283914], 'label': '77760.bo.360.bf2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.bf2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bf2', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246057320
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '12.e1', '12.j1'], 'contains': ['48.a1', '72.k1', '72.l1', '120.bi1', '144.f1', '240.bq1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [479363884, 443555763388, 143975, 80880, 80787], 'label': '77760.bo.24.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1', 'subgroup_fusion': None, 'weyl_group': '4320.bp'}
  • id: 246057321
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.c1', '180.t1', '180.y1', '180.be1', '180.bg1', '180.bw1'], 'contains': ['720.bc1', '720.dv1', '720.dz1', '1080.x1', '1080.br1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [143975, 80787, 267845678885, 85805, 443120250115, 80880], 'label': '77760.bo.360.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.bg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bg1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057322
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.d1', '180.t1', '180.z1', '180.bf1', '180.bh1', '180.bi1', '180.br1', '180.bx1'], 'contains': ['720.bc1', '720.dw1', '720.dy1', '1080.y1', '1080.bs1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [88695170185, 482635561, 143975, 85805, 80880, 80787], 'label': '77760.bo.360.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.bh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bh1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057323
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.e1', '180.u1', '180.w1', '180.be1', '180.bq1', '180.bx1'], 'contains': ['720.bc1', '720.dx1', '720.dy1', '1080.z1', '1080.bt1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [482635561, 143975, 85805, 80880, 80787, 88695348625], 'label': '77760.bo.360.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.bi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bi1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057324
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.d1', '180.u1', '180.v1', '180.bf1', '180.bm1', '180.bw1'], 'contains': ['720.bc1', '720.dz1', '720.ea1', '1080.ba1', '1080.bu1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [267845679213, 443120250115, 143975, 85805, 80880, 80787], 'label': '77760.bo.360.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.bj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bj1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057325
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.v1', '180.x1', '180.x2', '180.bg1', '180.bi1', '180.bq1', '180.by1'], 'contains': ['720.bc1', '720.bk1', '720.dt1', '720.du1', '720.ft1', '1080.bb1', '1080.bv1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [274468060348, 143975, 268244570163, 85805, 80880, 80787], 'label': '77760.bo.360.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.bk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bk1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057326
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.h1', '90.q1', '120.l1', '120.n1', '180.bt1'], 'contains': ['720.bd1', '720.be1', '720.bf1', '720.eb1', '720.ed1', '720.ez1', '720.fc1', '1080.bc1', '1080.bd1', '1080.bq1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [183845, 442641386852, 143975, 997965813, 519235320, 80787], 'label': '77760.bo.360.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '360.bl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bl1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057327
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.e1', '120.m1', '180.ba1', '180.bd1', '180.bj1', '180.bk1', '180.bo1', '180.bs1', '180.bu1'], 'contains': ['720.ef1', '1080.bf1', '1080.bh1', '1080.bw1', '1440.h1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [183845, 274467962404, 143975, 194518339175, 268244605587, 80787], 'label': '77760.bo.360.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '360.bm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bm1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246057328
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.m1', '180.bb1', '180.bl1', '180.bp1'], 'contains': ['720.eg1', '1080.bg1', '1080.bw1', '1440.i1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [442680946109, 355499025961, 355419504028, 85805, 80880, 80787], 'label': '77760.bo.360.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1', 'old_label': '360.bn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bn1', 'subgroup_fusion': None, 'weyl_group': '1296.2931'}
  • id: 246057329
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.m1', '180.y1', '180.bc1', '180.bm1', '180.bn1', '180.bq1', '180.br1', '180.by1'], 'contains': ['720.bc1', '720.dt1', '720.eh1', '1080.be1', '1080.bw1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [183845, 355499026316, 143975, 442681079189, 80880, 80787], 'label': '77760.bo.360.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '360.bo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bo1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057330
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.n1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.r1', '120.q1', '120.s1', '180.bt1'], 'contains': ['720.f1', '720.o1', '720.y1', '720.be1', '720.bl1', '720.bq1', '720.cc1', '1080.bi1', '1080.bl1', '1080.bx1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [174436554242, 143975, 375138270474, 85805, 80787, 143304], 'label': '77760.bo.360.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '360.bp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bp1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057332
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.s1', '120.q1', '120.t1', '180.bt1'], 'contains': ['720.g1', '720.r1', '720.bb1', '720.bf1', '720.bl1', '720.bs1', '720.cf1', '1080.bj1', '1080.bm1', '1080.bx1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [188331270027, 143975, 375138270474, 85805, 80787, 143304], 'label': '77760.bo.360.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '360.bq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bq1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057333
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.i1', '90.t1', '120.r1', '120.u1', '180.bt1'], 'contains': ['720.k1', '720.t1', '720.bd1', '720.bi1', '720.bl1', '720.by1', '720.cg1', '1080.bk1', '1080.bn1', '1080.by1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [368392152811, 442637475987, 85805, 80880, 80787, 693], 'label': '77760.bo.360.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '360.br1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.br1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057334
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gk1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.s1', '120.t1', '180.bv1', '180.bv2'], 'contains': ['720.a1', '720.ba1', '720.bh1', '720.cj1', '720.cl1', '1080.bx1'], 'core': '720.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [143975, 375138270474, 85805, 80880, 80787, 143304], 'label': '77760.bo.360.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '360.bs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bs1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246057335
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1', '120.u1', '180.bv1', '180.bv2', '180.bw1', '180.bx1', '180.by1'], 'contains': ['720.a1', '720.bc1', '720.bk1', '720.ck1', '720.cm1', '1080.by1'], 'core': '720.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [143975, 85805, 80880, 80787, 274467916948, 143304], 'label': '77760.bo.360.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.bt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bt1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246057336
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.v1', '180.r1'], 'contains': ['720.bm1', '720.bo1', '720.bp1', '720.dc1', '720.fe1', '1080.bz1', '1080.ca1', '1080.cb1', '1080.cc1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [174400208787, 93448938387, 456053150130, 180587272349, 45813, 80787], 'label': '77760.bo.360.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.r1', 'old_label': '360.bu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bu1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057337
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.w1', '120.x1', '180.r1', '180.bz1', '180.ca1'], 'contains': ['720.bm1', '720.bn1', '720.dj1', '720.do1', '720.en1', '1080.cd1', '1080.ce1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [80787, 174400208787, 93448938387, 180587232000, 45813, 83543730], 'label': '77760.bo.360.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '360.bv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bv1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246057338
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.y1', '180.r1', '180.bz1', '180.cb1'], 'contains': ['720.bn1', '720.bo1', '720.el1', '720.fp1', '1080.cf1', '1080.ch1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [83548555, 174400208787, 93448938387, 180587232000, 80787, 693], 'label': '77760.bo.360.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '360.bw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bw1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057339
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1', '120.z1', '120.bb1', '180.s1', '180.ca1', '180.cb1'], 'contains': ['720.bn1', '720.eq1', '720.er1', '1080.ci1', '3240.by1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [280259481600, 482854444, 88695353644, 193999455627, 80787, 143304], 'label': '77760.bo.360.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '360.bx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bx1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246057340
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.ba1', '180.s1', '180.bz1'], 'contains': ['720.bn1', '720.es1', '1080.cj1', '3240.bz1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [482808988, 280259481600, 224184, 193999500984, 80787, 88695348625], 'label': '77760.bo.360.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '360.by1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.by1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057341
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.z1', '120.v1', '120.bc1', '180.bt1'], 'contains': ['720.bq1', '720.cf1', '720.cg1', '720.cn1', '720.cq1', '720.fc1', '720.fr1', '1080.bz1', '1080.ck1', '1080.cl1', '1080.cm1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [442641386187, 224184, 143975, 998139594, 519235320, 80787], 'label': '77760.bo.360.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '360.bz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bz1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057342
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.e1', '12.f1', '12.j1'], 'contains': ['48.a1', '72.o1', '72.p1', '120.bs1', '144.h1', '240.bu1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [174879492452, 462320323891, 143975, 80880, 80787], 'label': '77760.bo.24.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1', 'subgroup_fusion': None, 'weyl_group': '4320.bp'}
  • id: 246057343
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['90.ba1', '120.v1', '120.bd1', '180.bt1'], 'contains': ['720.bs1', '720.cc1', '720.cg1', '720.cx1', '720.da1', '720.ez1', '720.ff1', '1080.ca1', '1080.ck1', '1080.cp1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [518964004, 997965504, 442641109705, 80880, 80787, 143304], 'label': '77760.bo.360.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '360.ca1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ca1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057344
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.v1'], 'contains': ['720.bu1', '720.cd1', '720.ch1', '720.cy1', '720.dd1', '720.fa1', '720.fi1', '1080.cb1', '1080.cm1', '1080.cp1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1440, 'diagramx': None, 'generators': [180587317946, 83467916, 174400208880, 93448938480, 148, 693], 'label': '77760.bo.360.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.cb1', 'old_label': '360.cb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cb1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057345
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.v1', '180.p1'], 'contains': ['720.bv1', '720.ce1', '720.ci1', '720.cz1', '720.de1', '720.fb1', '720.fj1', '1080.cc1', '1080.cl1', '1080.cp1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [93448857748, 456053069398, 148, 180587272349, 174400128148, 693], 'label': '77760.bo.360.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.p1', 'old_label': '360.cc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cc1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057346
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.l1', '90.bb1', '120.w1', '120.be1', '180.bt1'], 'contains': ['720.bq1', '720.bs1', '720.by1', '720.cr1', '720.df1', '720.dm1', '720.ed1', '1080.cd1', '1080.cn1', '1080.cq1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [442641386187, 998099012, 143975, 519235320, 80787, 143304], 'label': '77760.bo.360.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '360.cd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cd1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057347
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.m1', '90.bc1', '120.x1', '120.be1'], 'contains': ['720.br1', '720.bt1', '720.bz1', '720.cu1', '720.dg1', '720.dn1', '720.ee1', '1080.cd1', '1080.co1', '1080.cr1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [224184, 375138311012, 368871373412, 174436559403, 80787, 179159], 'label': '77760.bo.360.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.ce1', 'old_label': '360.ce1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ce1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246057348
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.w1', '180.p1', '180.cg1', '180.ch1'], 'contains': ['720.bv1', '720.ca1', '720.dk1', '720.dp1', '720.eo1', '1080.ce1', '1080.cq1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [93449082115, 224184, 456053069398, 174400128000, 224515, 180587232000], 'label': '77760.bo.360.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '360.cf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cf1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057349
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.x1', '180.ci1'], 'contains': ['720.bx1', '720.cb1', '720.dl1', '720.dq1', '720.ep1', '1080.ce1', '1080.cr1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [178680, 83462998, 174400128000, 93449036759, 180587232000, 179159], 'label': '77760.bo.360.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.s1', 'old_label': '360.cg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cg1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057369
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.l1', '180.bx1', '180.cq1', '180.ct1', '180.cy1', '180.de1'], 'contains': ['720.ck1', '720.dy1', '1080.cw1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [482808988, 143975, 80880, 80787, 88695348625, 143304], 'label': '77760.bo.360.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.cu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cu1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057350
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.n1', '90.bd1', '120.y1', '120.bf1', '180.bt1'], 'contains': ['720.by1', '720.cc1', '720.cf1', '720.eb1', '720.ec1', '720.fl1', '720.fs1', '1080.cf1', '1080.cs1', '1080.da1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 720, 'diagramx': None, 'generators': [224184, 442641300629, 143975, 998139594, 519235320, 80787], 'label': '77760.bo.360.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.bt1', 'old_label': '360.ch1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ch1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057351
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.g1', '120.bg1', '180.bu1', '180.cc1', '180.ce1', '180.cj1', '180.ck1', '180.cl1', '180.cn1'], 'contains': ['720.ef1', '1080.cg1', '1080.db1', '1080.dd1', '1080.de1', '1440.k1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [80787, 268244570163, 143304, 194518275844, 274467916948, 80880], 'label': '77760.bo.360.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '360.ci1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ci1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246057352
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.h1', '120.bg1', '180.cd1', '180.cf1', '180.co1'], 'contains': ['720.ei1', '1080.cg1', '1080.dc1', '1080.df1', '1080.dg1', '1440.l1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [274467962404, 268244605587, 194518419812, 80787, 143304, 179159], 'label': '77760.bo.360.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '360.cj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cj1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057353
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['6.a1', '6.b1', '6.c1', '6.d1', '6.e1', '6.g1', '6.i1', '9.a1', '9.b1', '18.i1', '30.e1', '45.a1'], 'core': '6.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [143975, 85805, 93924236159, 80787, 462320328386, 143304], 'label': '77760.bo.3.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '3.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': '25920.w'}
  • id: 246057354
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.i1', '12.l1', '12.o1'], 'contains': ['72.a1', '72.r1', '144.j1', '240.ce1', '360.gh1'], 'core': '72.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [87182201544, 274511462400, 80787, 179159], 'label': '77760.bo.24.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '24.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
  • id: 246057355
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.y1', '180.p1', '180.cg1', '180.cm1'], 'contains': ['720.ca1', '720.ce1', '720.ek1', '720.em1', '720.fk1', '1080.ch1', '1080.da1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [83548555, 174400128000, 143975, 180587232000, 93449001575, 143304], 'label': '77760.bo.360.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '360.ck1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ck1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057356
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.o1', '120.z1', '180.q1', '180.ch1', '180.cm1'], 'contains': ['720.ca1', '720.et1', '720.eu1', '1080.ci1', '3240.cl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [482854584, 88695272904, 280259527104, 80880, 193999420104, 143304], 'label': '77760.bo.360.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '360.cl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cl1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057357
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.ba1', '180.q1', '180.cg1'], 'contains': ['720.ca1', '720.ev1', '720.ew1', '1080.cj1', '3240.cm1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [280259481600, 482854584, 224184, 224515, 193999277398, 88695348625], 'label': '77760.bo.360.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '360.cm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cm1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057358
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1', '120.bb1', '180.ci1'], 'contains': ['720.cb1', '720.ex1', '720.ey1', '1080.ci1', '3240.cp1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [193999277250, 280259481600, 143731, 88695272904, 482773704, 143304], 'label': '77760.bo.360.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.s1', 'old_label': '360.cn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cn1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057359
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.bc1', '120.bd1', '180.bv1', '180.cp1', '180.cp2'], 'contains': ['720.cj1', '720.cl1', '720.cm1', '720.cp1', '720.fh1', '1080.ck1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [87182277597, 143975, 375138270474, 80880, 80787, 143304], 'label': '77760.bo.360.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.x1', 'old_label': '360.co1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.co1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246057360
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.co2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.bv2', '180.cp1', '180.cp2'], 'contains': ['720.cj1', '720.cl1', '720.cm1', '720.cp2', '720.fh2', '1080.ck2'], 'core': '1440.b1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [448908278999, 442641300482, 143975, 80880, 80787, 143304], 'label': '77760.bo.360.co2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.co2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.co2', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246057361
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.be1', '180.bv1', '180.cp2', '180.cq1', '180.cr1', '180.cu1', '180.cv1', '180.cw1'], 'contains': ['720.cj1', '720.ck1', '720.ct1', '720.cw1', '720.ds1', '1080.cn1', '1080.co1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [143975, 80787, 143304, 442641386424, 443120250115, 80880], 'label': '77760.bo.360.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.cp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cp1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057362
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.cp2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.gh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bv2', '180.cp1', '180.cs1', '180.ct1', '180.cw1'], 'contains': ['720.cj1', '720.ck1', '720.ct2', '720.cw2', '720.ds2', '1080.cn2', '1080.co2'], 'core': '1440.b1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [448908278999, 442641386424, 143975, 80880, 80787, 143304], 'label': '77760.bo.360.cp2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.cp2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cp2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246057363
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.bf1', '180.bv1', '180.cp1', '180.cq1', '180.cx1', '180.da1', '180.dc1', '180.dd1'], 'contains': ['720.ck1', '720.cl1', '720.dr1', '720.fn1', '1080.cs1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [143975, 80787, 143304, 443120250115, 442641300482, 80880], 'label': '77760.bo.360.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.cq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cq1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057364
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.cq2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bv2', '180.cp2', '180.cy1', '180.cz1', '180.dd1'], 'contains': ['720.ck1', '720.cl1', '720.dr2', '720.fn2', '1080.cs2'], 'core': '1440.b1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [143975, 80787, 143304, 442641300482, 448908283914, 80880], 'label': '77760.bo.360.cq2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.cq2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cq2', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246057365
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1', '9.b1'], 'contains': ['54.a1', '54.b1', '54.c1', '54.f1', '54.g1', '162.a1', '270.e1', '405.a1'], 'core': '108.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [5066, 93924236159, 462320011466, 693], 'label': '77760.bo.27.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '27.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1', 'subgroup_fusion': None, 'weyl_group': '720.763'}
  • id: 246057366
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.by1', '180.cp1', '180.cp2', '180.cr1', '180.cx1', '180.db1', '180.de1'], 'contains': ['720.ck1', '720.cm1', '720.dt1', '720.ft1', '1080.ct1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [143975, 268244570163, 274468002505, 80880, 80787, 143304], 'label': '77760.bo.360.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.cr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cr1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057367
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.i1', '180.bw1', '180.cs1', '180.cu1', '180.cx1', '180.cy1'], 'contains': ['720.ck1', '720.dv1', '720.ea1', '1080.cu1', '1080.cy1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [143975, 80787, 267845674052, 143304, 443120250115, 80880], 'label': '77760.bo.360.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.cs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cs1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057368
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.k1', '180.bx1', '180.cs1', '180.cv1', '180.cz1', '180.da1', '180.db1', '180.df1'], 'contains': ['720.ck1', '720.dw1', '720.dx1', '1080.cv1', '1080.cz1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [482808988, 143975, 88695353644, 80880, 80787, 143304], 'label': '77760.bo.360.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.ct1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ct1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057370
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.j1', '180.bw1', '180.cr1', '180.ct1', '180.cz1', '180.dc1'], 'contains': ['720.ck1', '720.dz1', '1080.cx1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [267845679213, 443120250115, 143975, 80880, 80787, 143304], 'label': '77760.bo.360.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.cv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cv1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057371
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.bg1', '180.by1', '180.cu1', '180.cw1', '180.dc1', '180.dd1', '180.de1', '180.df1'], 'contains': ['720.ck1', '720.du1', '720.eh1', '1080.db1', '1080.dc1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [442681119480, 355499200051, 143975, 80880, 80787, 143304], 'label': '77760.bo.360.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '360.cw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cw1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057372
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.x1', '180.x2', '180.cp2'], 'contains': ['720.cp1', '720.cp2', '720.ct1', '720.fh1', '720.fh2', '720.fn2', '720.ft1', '1080.dh1', '1080.dh2'], 'core': '2880.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [461841090505, 143975, 19679125948, 80880, 80787, 462320328386], 'label': '77760.bo.360.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.x1', 'old_label': '360.cx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cx1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246057373
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.cx2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.x1', '180.cp1'], 'contains': ['720.cp2', '720.ct2', '720.fh1', '720.fn1', '720.ft1', '1080.dh3'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [19679068105, 143975, 80880, 80787, 448908283914, 462320328386], 'label': '77760.bo.360.cx2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.x1', 'old_label': '360.cx2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cx2', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246057374
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.cx3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.x2', '180.cp1'], 'contains': ['720.cp1', '720.ct2', '720.fh2', '720.fn1', '720.ft1', '1080.dh4'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841090505, 462320323891, 143975, 19679125948, 80880, 80787], 'label': '77760.bo.360.cx3', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.x1', 'old_label': '360.cx3', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cx3', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 246057375
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.x1', '180.bc1', '180.cp1', '180.dg1', '180.dj1', '180.dk1', '180.ds1'], 'contains': ['720.cp1', '720.cp2', '720.cw2', '720.dr1', '720.dt1', '1080.di1', '1080.dk1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841090505, 462320323320, 143975, 19678982548, 80880, 80787], 'label': '77760.bo.360.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.cy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cy1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057376
    {'ambient': '77760.bo', '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': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['15.a1'], 'contains': ['60.d1', '60.i1', '60.j1', '60.ba1', '60.bb1', '60.bf1', '60.bh1', '90.a1', '90.j1', '90.k1', '90.l1', '120.f1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [461841090505, 143975, 80787, 85805, 19678982548, 262496684612, 448908283914, 80880, 462320328386], 'label': '77760.bo.30.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '30.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.a1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246057377
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.cy2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.x2', '180.bc1', '180.cp2', '180.dh1', '180.di1', '180.dm1', '180.do1'], 'contains': ['720.cp1', '720.cp2', '720.cw1', '720.dr2', '720.dt1', '1080.di2', '1080.dk2'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 19678982548, 461841188401, 462320328958, 80880, 80787], 'label': '77760.bo.360.cy2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.cy2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cy2', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057378
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.m1', '180.w1', '180.z1', '180.cq1', '180.dg2', '180.di1', '180.dm1', '180.ds1'], 'contains': ['720.cw1', '720.dr1', '720.dy1', '1080.dj1', '1080.dl1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [456053074316, 87262035243, 143975, 83641651, 80880, 80787], 'label': '77760.bo.360.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.cz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cz1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057379
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.x1', '180.cw1', '180.dg1', '180.dl1', '180.dw1'], 'contains': ['720.ct1', '720.ct2', '720.cw2', '720.ds1', '720.du1', '1080.dm1', '1080.dn1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [462320323320, 143975, 461841148348, 19678982548, 80880, 80787], 'label': '77760.bo.360.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.da1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.da1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057380
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.da2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.x2', '180.cw1', '180.dg2', '180.dn1', '180.dp1'], 'contains': ['720.ct1', '720.ct2', '720.cw1', '720.ds2', '720.du1', '1080.dm2', '1080.dn2'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [462320323891, 143975, 461841148348, 19678982548, 80880, 80787], 'label': '77760.bo.360.da2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.da2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.da2', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057381
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.n1', '180.w1', '180.cv1', '180.dh1', '180.dn1', '180.dw1'], 'contains': ['720.cw1', '720.ds1', '720.dx1', '1080.do1', '1080.dp1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [87262035243, 143975, 83641651, 456053150130, 80880, 80787], 'label': '77760.bo.360.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.db1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.db1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057382
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.v1', '180.y1', '180.cr1', '180.dg2', '180.dh1', '180.do1', '180.ds1'], 'contains': ['720.cw1', '720.dt1', '720.dz1', '1080.dq1', '1080.dr1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 87182201788, 482768881, 80880, 80787, 375138230375], 'label': '77760.bo.360.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.dc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.dc1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057383
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.v1', '180.cu1', '180.di1', '180.dp1', '180.dw1'], 'contains': ['720.cw1', '720.du1', '720.ea1', '1080.ds1', '1080.dt1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [482808988, 143975, 87182201788, 80880, 80787, 375138230375], 'label': '77760.bo.360.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.dd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.dd1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057384
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.t1', '180.cs1', '180.dj1', '180.dl1', '180.ed1'], 'contains': ['720.cw2', '720.dv1', '720.dw1', '1080.du1', '1080.dy1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [7185104880, 462320323320, 143975, 19678982548, 80880, 80787], 'label': '77760.bo.360.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.de1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.de1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057385
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.u1', '180.cs1', '180.dk1', '180.dw1'], 'contains': ['720.cw2', '720.dx1', '720.ea1', '1080.dv1', '1080.dz1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [462320323320, 143975, 19678982548, 80880, 80787, 7185202680], 'label': '77760.bo.360.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.df1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.df1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057386
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.t1', '180.u1', '180.ct1', '180.dg1', '180.ds1'], 'contains': ['720.cw2', '720.dy1', '720.dz1', '1080.dw1', '1080.dx1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [462320323320, 7185162389, 143975, 19678982548, 80880, 80787], 'label': '77760.bo.360.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.dg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.dg1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057387
    {'ambient': '77760.bo', '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': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['15.a1'], 'contains': ['60.e1', '60.h1', '60.j1', '60.bc1', '60.bd1', '60.bg1', '60.bh1', '90.b1', '90.h1', '90.m1', '120.i1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [143975, 80787, 355462871189, 87660962042, 375138270474, 482635561, 183845, 80880, 462320328386], 'label': '77760.bo.30.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '30.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246057388
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.bi1', '180.y1', '180.cu1', '180.dm1', '180.dn1', '180.ed1'], 'contains': ['720.cw1', '720.dv1', '720.eh1', '1080.ea1', '1080.eb1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [143975, 80787, 442641386424, 443120250115, 80880, 180667065843], 'label': '77760.bo.360.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.dh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.dh1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057389
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.o1', '180.z1', '180.cv1', '180.do1', '180.dp1', '180.ed1'], 'contains': ['720.cw1', '720.dw1', '1080.ec1', '1080.ed1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [87262035243, 143975, 83641651, 456053248051, 80880, 80787], 'label': '77760.bo.360.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.di1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.di1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057390
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bh1', '180.d1', '180.ba1', '180.cc1', '180.dq1', '180.dt1', '180.du1', '180.ee1'], 'contains': ['720.ef1', '1080.ee1', '1080.eg1', '1080.eh1', '1080.ej1', '1080.ek1', '1440.q1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [462320323320, 19679028004, 143975, 461841050404, 262496684612, 80787], 'label': '77760.bo.360.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '360.dj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.dj1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246057391
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bh1', '180.bb1', '180.dr1', '180.dv1'], 'contains': ['720.eg1', '1080.ee1', '1080.eh1', '1080.ei1', '1440.r1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [262496649331, 462320323320, 19679028004, 143975, 461841050404, 80787], 'label': '77760.bo.360.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1', 'old_label': '360.dk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.dk1', 'subgroup_fusion': None, 'weyl_group': '432.747'}
  • id: 246057392
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.bh1', '180.bc1', '180.cw1', '180.ds1', '180.dw1', '180.ed1'], 'contains': ['720.cw1', '720.cw2', '720.eh1', '1080.ee1', '1080.ef1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [461841004948, 462320323320, 143975, 19678982548, 80880, 80787], 'label': '77760.bo.360.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '360.dl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.dl1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057393
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.bh1', '180.cd1', '180.dx1', '180.ef1'], 'contains': ['720.ei1', '1080.ef1', '1080.eg1', '1080.ei1', '1080.el1', '1080.em1', '1440.t1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [355462732800, 462320323467, 375138311012, 87661002387, 80787, 179159], 'label': '77760.bo.360.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.k1', 'old_label': '360.dm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.dm1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057394
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.bh1', '180.dy1'], 'contains': ['720.ej1', '1080.ef1', '1080.eh1', '1080.ei1', '1440.u1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [462320323467, 375138311012, 355462813680, 87661002387, 80787, 179159], 'label': '77760.bo.360.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.bb1', 'old_label': '360.dn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.dn1', 'subgroup_fusion': None, 'weyl_group': '216.165'}
  • id: 246057395
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.k1', '120.bi1', '180.e1', '180.bd1', '180.ce1', '180.dz1', '180.ea1', '180.eb1', '180.ee1'], 'contains': ['720.ef1', '1080.ea1', '1080.en1', '1080.eo1', '1440.v1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [442641386187, 180667146387, 443120250115, 143975, 442162022400, 80787], 'label': '77760.bo.360.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '360.do1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.do1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246057396
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.l1', '120.bi1', '180.cf1', '180.ec1', '180.ef1'], 'contains': ['720.ei1', '1080.eb1', '1080.en1', '1080.ep1', '1440.w1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [188331171987, 87182201544, 482676004, 375138311012, 80787, 179159], 'label': '77760.bo.360.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.k1', 'old_label': '360.dp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.dp1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057397
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bj1', '180.b1', '180.f1', '180.cg1'], 'contains': ['720.dp1', '720.ek1', '720.ev1', '1080.eq1', '3240.cv1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [93449082115, 83601118, 174400128000, 224515, 456053293315, 180587232000], 'label': '77760.bo.360.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '360.dq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.dq1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246057398
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.a1', '15.a1'], 'contains': ['60.d1', '60.e1', '60.l1', '60.ba1', '60.bc1', '60.be1', '60.bi1', '90.c1', '90.n1', '90.o1', '120.j1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [461841090505, 448908283441, 143975, 19678982548, 85805, 262496684612, 80880, 80787, 462320328386], 'label': '77760.bo.30.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '30.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.c1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246057399
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bj1', '120.bk1', '180.g1', '180.h1', '180.bz1'], 'contains': ['720.do1', '720.el1', '720.es1', '1080.eq1', '3240.cy1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [456053068800, 174400208787, 93448938387, 180587232000, 80787, 83467561], 'label': '77760.bo.360.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '360.dr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.dr1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057400
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bk1', '180.a1', '180.i1', '180.cg1'], 'contains': ['720.dp1', '720.em1', '720.ew1', '1080.eq1', '3240.cz1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [83548555, 93449036612, 179012, 456053247812, 174400128000, 180587232000], 'label': '77760.bo.360.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '360.ds1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ds1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057401
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.bl1', '120.bm1', '180.g1', '180.ca1'], 'contains': ['720.do1', '720.en1', '720.er1', '1080.er1', '3240.db1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [174400208787, 93448938387, 456053150130, 83462400, 180587232000, 80787], 'label': '77760.bo.360.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '360.dt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.dt1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246057402
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bl1', '180.a1', '180.f1', '180.ch1'], 'contains': ['720.dp1', '720.eo1', '720.eu1', '1080.er1', '3240.de1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [93449082115, 83462998, 174400128000, 224515, 456053293315, 180587232000], 'label': '77760.bo.360.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '360.du1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.du1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057403
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.bm1', '180.ci1'], 'contains': ['720.dq1', '720.ep1', '720.ey1', '1080.er1', '3240.df1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [83462998, 174400128000, 93449036759, 180587232000, 456053247959, 179159], 'label': '77760.bo.360.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.s1', 'old_label': '360.dv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.dv1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057404
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '120.bn1', '120.bo1', '180.h1', '180.ca1'], 'contains': ['720.do1', '720.eq1', '1080.es1', '3240.dy1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 10, 'diagramx': None, 'generators': [456053068800, 174400208787, 93448938387, 83462400, 180587232000, 80787], 'label': '77760.bo.360.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '360.dw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.dw1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246057405
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.q1', '120.bn1', '180.b1', '180.i1', '180.ch1'], 'contains': ['720.dp1', '720.et1', '1080.es1', '3240.dz1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [180587277504, 456053114304, 83507904, 174400208880, 93448938480, 80880], 'label': '77760.bo.360.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '360.dx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.dx1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246057406
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.r1', '120.bo1', '180.ci1'], 'contains': ['720.dq1', '720.ex1', '1080.es1', '3240.ea1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [83641559, 174400128000, 93449036759, 180587232000, 456053247959, 179159], 'label': '77760.bo.360.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.s1', 'old_label': '360.dy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.dy1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246057407
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.x1', '180.bn1', '180.cp2', '180.dh1', '180.eg1', '180.eh1', '180.eq1'], 'contains': ['720.dr2', '720.ds1', '720.dt1', '720.fh1', '720.fh2', '1080.et1', '1080.fd1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841090505, 143975, 19678982548, 462320328958, 80880, 80787], 'label': '77760.bo.360.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.dz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.dz1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057408
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.dz2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.x2', '180.bn1', '180.cp1', '180.dg2', '180.ei1', '180.ej1', '180.en1'], 'contains': ['720.dr1', '720.ds2', '720.dt1', '720.fh1', '720.fh2', '1080.et2', '1080.fd2'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841090505, 462320323891, 143975, 19678982548, 80880, 80787], 'label': '77760.bo.360.dz2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.dz2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.dz2', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057409
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '30.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.b1', '15.a1'], 'contains': ['60.h1', '60.i1', '60.l1', '60.bf1', '60.bg1', '60.bi1', '60.bj1', '90.d1', '90.p1', '90.q1', '120.l1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [183845, 355462871189, 87660962042, 143975, 375138270474, 482768881, 80880, 80787, 462320328386], 'label': '77760.bo.30.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '30.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.d1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246057410
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.p1', '180.w1', '180.bh1', '180.cq1', '180.dg1', '180.eh1', '180.en1', '180.eq1'], 'contains': ['720.dr1', '720.ds1', '720.dy1', '1080.eu1', '1080.fe1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [87262035243, 83467916, 143975, 456053150130, 80880, 80787], 'label': '77760.bo.360.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.ea1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ea1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057411
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.y1', '180.bg1', '180.cx1', '180.dj1', '180.dm1', '180.eh1', '180.ei1'], 'contains': ['720.dr1', '720.dt1', '720.dv1', '1080.ev1', '1080.fg1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 80787, 375138270474, 87182201788, 482635561, 80880], 'label': '77760.bo.360.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.eb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.eb1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057412
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.v1', '180.bm1', '180.cx1', '180.di1', '180.dk1', '180.ej1', '180.eq1'], 'contains': ['720.dr1', '720.dt1', '720.ea1', '1080.ew1', '1080.ff1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 375138270474, 87182201788, 482768881, 80880, 80787], 'label': '77760.bo.360.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.ec1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ec1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057413
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.v1', '180.bg1', '180.dc1', '180.dg1', '180.dg2', '180.ek1', '180.eu1'], 'contains': ['720.dr1', '720.du1', '720.dz1', '1080.ex1', '1080.fh1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [180667209003, 443120250115, 143975, 442641300958, 80880, 80787], 'label': '77760.bo.360.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.ed1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ed1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057414
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.t1', '180.be1', '180.cy1', '180.dm1', '180.eh1'], 'contains': ['720.dr2', '720.dv1', '720.dy1', '1080.ey1', '1080.fi1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [7185104880, 143975, 19678982548, 462320328958, 80880, 80787], 'label': '77760.bo.360.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.ee1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ee1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057415
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.t1', '180.bf1', '180.cz1', '180.do1', '180.eg1', '180.ek1', '180.ew1'], 'contains': ['720.dr2', '720.dw1', '720.dz1', '1080.ez1', '1080.fj1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [7185162389, 143975, 19678982548, 462320328958, 80880, 80787], 'label': '77760.bo.360.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.ef1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ef1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057416
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.u1', '180.be1', '180.cz1', '180.dh1', '180.eu1'], 'contains': ['720.dr2', '720.dx1', '720.dz1', '1080.fa1', '1080.fk1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [7185029309, 143975, 19678982548, 462320328958, 80880, 80787], 'label': '77760.bo.360.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.eg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.eg1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057417
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.u1', '180.bf1', '180.cy1', '180.di1', '180.eq1'], 'contains': ['720.dr2', '720.dy1', '720.ea1', '1080.fb1', '1080.fl1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [143975, 19678982548, 462320328958, 80880, 80787, 7185202680], 'label': '77760.bo.360.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.eh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.eh1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057418
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.x1', '180.x2', '180.dd1', '180.di1', '180.eh1', '180.ek1', '180.eu1'], 'contains': ['720.dr1', '720.dr2', '720.du1', '720.fn1', '720.fn2', '1080.fm1', '1080.fm2'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 461841148348, 19678982548, 462320328958, 80880, 80787], 'label': '77760.bo.360.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.ei1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ei1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057419
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.q1', '180.z1', '180.bh1', '180.da1', '180.dj1', '180.ej1', '180.ek1', '180.ew1'], 'contains': ['720.dr1', '720.dw1', '1080.fc1', '1080.fo1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [456053074316, 87262035243, 83467916, 143975, 80880, 80787], 'label': '77760.bo.360.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.ej1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ej1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057420
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '30.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3.a1', '10.a1'], 'contains': ['60.a1', '60.b1', '60.c1', '60.f1', '60.g1', '60.k1', '60.m1', '60.n1', '60.q1', '60.r1', '60.t1', '90.e1', '90.f1', '270.bi1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [180587277504, 456053074316, 93448857748, 83543730, 174400173363, 85805, 80880, 80787, 693], 'label': '77760.bo.30.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '30.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.e1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 246057421
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.r1', '180.w1', '180.da1', '180.dk1', '180.ei1', '180.eu1'], 'contains': ['720.dr1', '720.dx1', '1080.fn1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [456053207518, 87262035243, 83467916, 143975, 80880, 80787], 'label': '77760.bo.360.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.ek1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ek1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057422
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.bg1', '180.bm1', '180.cr1', '180.dg1', '180.dh1', '180.eg1', '180.en1'], 'contains': ['720.ds1', '720.dt1', '720.dz1', '1080.fp1', '1080.fq1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 80787, 180667151546, 442641386755, 443120250115, 80880], 'label': '77760.bo.360.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.el1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.el1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057423
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.bg1', '180.cu1', '180.dl1', '180.dn1', '180.eh1'], 'contains': ['720.ds1', '720.du1', '720.dv1', '1080.fr1', '1080.fs1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [180667209003, 442641386755, 443120250115, 143975, 80880, 80787], 'label': '77760.bo.360.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.em1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.em1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057424
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.be1', '180.cs1', '180.dn1', '180.ei1'], 'contains': ['720.ds2', '720.dv1', '720.dx1', '1080.ft1', '1080.fx1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [7185104880, 462320323891, 143975, 19678982548, 80880, 80787], 'label': '77760.bo.360.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.en1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.en1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057425
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bf1', '180.cs1', '180.dp1', '180.ej1', '180.ex1'], 'contains': ['720.ds2', '720.dw1', '720.ea1', '1080.fu1', '1080.fy1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [462320323891, 143975, 19678982548, 80880, 80787, 7185202680], 'label': '77760.bo.360.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.eo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.eo1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057426
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.be1', '180.bf1', '180.ct1', '180.dg2', '180.en1'], 'contains': ['720.ds2', '720.dy1', '720.dz1', '1080.fv1', '1080.fw1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [7185029309, 462320323891, 143975, 19678982548, 80880, 80787], 'label': '77760.bo.360.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.ep1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ep1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057427
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.s1', '180.bh1', '180.cv1', '180.dl1', '180.eg1', '180.ex1'], 'contains': ['720.ds1', '720.dw1', '1080.fz1', '1080.ga1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [87262035243, 83543730, 143975, 456053150130, 80880, 80787], 'label': '77760.bo.360.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.eq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.eq1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057428
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.bi1', '180.bq1', '180.de1', '180.dg1', '180.dg2', '180.di1', '180.eh1'], 'contains': ['720.dt1', '720.du1', '720.dy1', '1080.gb1', '1080.gd1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [87182202116, 143975, 355938110909, 374659447224, 80880, 80787], 'label': '77760.bo.360.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.er1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.er1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057429
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.bi1', '180.br1', '180.db1', '180.dj1', '180.do1', '180.eg1', '180.ej1'], 'contains': ['720.dt1', '720.dw1', '1080.gc1', '1080.gf1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [87182277125, 143975, 355938110909, 374659447224, 80880, 80787], 'label': '77760.bo.360.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.es1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.es1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057430
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.bq1', '180.db1', '180.dh1', '180.dk1', '180.ei1'], 'contains': ['720.dt1', '720.dx1', '1080.ge1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [143975, 80787, 87182277125, 374659447224, 355938243989, 80880], 'label': '77760.bo.360.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.et1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.et1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057431
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '30.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['15.a1'], 'contains': ['60.d1', '60.h1', '60.p1', '60.u1', '60.w1', '90.r1', '90.x1', '120.s1'], 'core': '720.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [461841090505, 143975, 80787, 262496586694, 143304, 85805, 19678982548, 80880, 462320328386], 'label': '77760.bo.30.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '30.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.f1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246057432
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bi1', '180.df1', '180.dl1', '180.dp1', '180.ek1'], 'contains': ['720.du1', '720.dw1', '1080.gg1', '1080.gh1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [355938284280, 87182202116, 143975, 374659447224, 80880, 80787], 'label': '77760.bo.360.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.eu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.eu1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057433
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bp1', '180.d1', '180.bj1', '180.cj1', '180.dz1', '180.el1', '180.ev1', '180.ey1'], 'contains': ['720.ef1', '1080.gi1', '1080.gm1', '1080.gn1', '1080.go1', '1440.bk1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [355462732800, 87660926666, 143975, 375138270474, 80787, 462320328386], 'label': '77760.bo.360.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '360.ev1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ev1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246057434
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.m1', '120.bq1', '180.e1', '180.bk1', '180.ck1', '180.dq1', '180.em1', '180.es1', '180.ey1'], 'contains': ['720.ef1', '1080.gj1', '1080.gk1', '1080.gl1', '1080.gr1', '1440.bn1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [482711044, 188331136563, 375138172555, 80880, 80787, 87182000787], 'label': '77760.bo.360.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '360.ew1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ew1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246057435
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bq1', '180.bl1', '180.dr1', '180.et1'], 'contains': ['720.eg1', '1080.gj1', '1080.gs1', '1440.bp1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [482711044, 188331315812, 375138172555, 80880, 80787, 87182000787], 'label': '77760.bo.360.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.k1', 'old_label': '360.ex1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ex1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
  • id: 246057436
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bq1', '180.y1', '180.bm1', '180.dc1', '180.ds1', '180.en1', '180.eu1', '180.ew1'], 'contains': ['720.dr1', '720.dz1', '720.eh1', '1080.gj1', '1080.gq1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [482711044, 143975, 375138270474, 87182201788, 80880, 80787], 'label': '77760.bo.360.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.ey1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ey1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057437
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bp1', '180.j1', '180.ba1', '180.cj1', '180.ea1', '180.eo1', '180.es1', '180.ez1'], 'contains': ['720.ef1', '1080.gn1', '1080.gp1', '1080.gv1', '1440.bo1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [143975, 461841050404, 80787, 19679028004, 462320328958, 262496684612], 'label': '77760.bo.360.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '360.ez1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ez1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246057438
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bp1', '180.bb1', '180.ep1', '180.et1'], 'contains': ['720.eg1', '1080.go1', '1080.gv1', '1440.bq1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [87660962042, 355462911959, 375138172205, 80880, 80787, 462320046985], 'label': '77760.bo.360.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1', 'old_label': '360.fa1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.fa1', 'subgroup_fusion': None, 'weyl_group': '1296.2931'}
  • id: 246057439
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bp1', '180.bc1', '180.bn1', '180.dd1', '180.dm1', '180.eq1', '180.eu1', '180.ew1'], 'contains': ['720.dr1', '720.dr2', '720.eh1', '1080.gm1', '1080.gv1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [461841004948, 143975, 19678982548, 80880, 80787, 462320328386], 'label': '77760.bo.360.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '360.fb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.fb1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057440
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.n1', '120.bq1', '180.k1', '180.bd1', '180.ck1', '180.dt1', '180.er1', '180.ev1', '180.ez1'], 'contains': ['720.ef1', '1080.gq1', '1080.gr1', '1080.gs1', '1080.gt1', '1080.gu1', '1440.by1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [180667146387, 443120250115, 143975, 442162022400, 442641301050, 80787], 'label': '77760.bo.360.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '360.fc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.fc1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246057441
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.br1', '180.j1', '180.bj1', '180.cc1', '180.eb1', '180.em1', '180.er1', '180.fa1'], 'contains': ['720.ef1', '1080.gw1', '1080.hc1', '1080.he1', '1080.hf1', '1440.bz1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [355462732800, 462320323891, 375138087093, 143975, 87661100427, 80787], 'label': '77760.bo.360.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '360.fd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.fd1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246057442
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '30.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.f1', '15.a1'], 'contains': ['60.e1', '60.i1', '60.p1', '60.v1', '60.x1', '90.s1', '90.v1', '120.t1'], 'core': '720.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [143975, 80787, 143304, 85805, 442641386424, 443120250115, 80880, 442162067904, 180667249346], 'label': '77760.bo.30.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '30.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.g1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246057443
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.br1', '180.cd1', '180.ec1', '180.fb1'], 'contains': ['720.ei1', '1080.gw1', '1080.hd1', '1080.hg1', '1080.hh1', '1440.ca1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [262496649331, 462320323891, 19679028004, 461841050404, 80787, 179159], 'label': '77760.bo.360.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '360.fe1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.fe1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057444
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.o1', '120.bs1', '180.k1', '180.bk1', '180.ce1', '180.du1', '180.el1', '180.eo1', '180.fa1'], 'contains': ['720.ef1', '1080.gx1', '1080.gz1', '1080.ha1', '1080.hi1', '1440.ce1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [482711044, 375138087093, 188331136563, 80880, 80787, 87182000787], 'label': '77760.bo.360.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '360.ff1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ff1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246057445
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bs1', '180.bl1', '180.dv1', '180.ep1'], 'contains': ['720.eg1', '1080.gx1', '1080.ha1', '1080.hb1', '1440.cf1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [180667146387, 442641386755, 443120250115, 143975, 442162067904, 80787], 'label': '77760.bo.360.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.k1', 'old_label': '360.fg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.fg1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057446
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.bs1', '180.bm1', '180.cu1', '180.dw1', '180.eq1', '180.ex1'], 'contains': ['720.ds1', '720.ea1', '720.eh1', '1080.gx1', '1080.gy1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [442641386755, 180667065843, 443120250115, 143975, 80880, 80787], 'label': '77760.bo.360.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.fh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.fh1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057447
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.p1', '120.bs1', '180.cf1', '180.dx1', '180.fb1'], 'contains': ['720.ei1', '1080.gy1', '1080.gz1', '1080.hb1', '1080.hj1', '1440.ch1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [188331171987, 87182201544, 482676004, 375138087093, 80787, 179159], 'label': '77760.bo.360.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '360.fi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.fi1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057448
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.bs1', '180.dy1'], 'contains': ['720.ej1', '1080.gy1', '1080.ha1', '1080.hb1', '1440.ci1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [443120204759, 180667146387, 442641386755, 442162067904, 80787, 179159], 'label': '77760.bo.360.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.dy1', 'old_label': '360.fj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.fj1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 246057449
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.br1', '180.bn1', '180.cw1', '180.dn1', '180.en1', '180.ex1'], 'contains': ['720.ds1', '720.ds2', '720.eh1', '1080.hc1', '1080.hd1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [461841004948, 462320323891, 143975, 19678982548, 80880, 80787], 'label': '77760.bo.360.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '360.fk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.fk1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057450
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bt1', '180.o1', '180.bo1', '180.cl1', '180.dq1', '180.dz1', '180.eo1', '180.er1'], 'contains': ['720.ef1', '1080.hk1', '1080.hl1', '1080.hm1', '1080.ho1', '1440.cn1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [262972240587, 87182277125, 355938105600, 143975, 374659446987, 80787], 'label': '77760.bo.360.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '360.fl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.fl1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246057451
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bt1', '180.bp1', '180.dr1', '180.ep1'], 'contains': ['720.eg1', '1080.hk1', '1080.hp1', '1440.co1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [80787, 87657511685, 87182000787, 19203926428, 80880, 374659084948], 'label': '77760.bo.360.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.k1', 'old_label': '360.fm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.fm1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
  • id: 246057452
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bt1', '180.bq1', '180.br1', '180.de1', '180.dm1', '180.ds1', '180.en1', '180.eq1'], 'contains': ['720.dt1', '720.dy1', '720.eh1', '1080.hk1', '1080.hn1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [143975, 87182201788, 355938110909, 374659447224, 80880, 80787], 'label': '77760.bo.360.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.fn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.fn1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057453
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '30.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.c1', '15.a1'], 'contains': ['60.j1', '60.l1', '60.p1', '60.y1', '60.z1', '90.t1', '90.y1', '120.u1'], 'core': '720.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [374659361758, 87182277597, 262972155450, 143975, 355938110909, 85805, 80880, 80787, 143304], 'label': '77760.bo.30.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '30.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.h1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246057454
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bt1', '180.l1', '180.bs1', '180.cl1', '180.dt1', '180.ea1', '180.el1', '180.em1'], 'contains': ['720.ef1', '1080.hn1', '1080.ho1', '1080.hp1', '1080.hq1', '1080.hr1', '1440.cs1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [87181925066, 355938186480, 262971878400, 374659084948, 80880, 80787], 'label': '77760.bo.360.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '360.fo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.fo1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246057455
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bu1', '180.l1', '180.bo1', '180.cn1', '180.du1', '180.eb1', '180.es1', '180.ev1'], 'contains': ['720.ef1', '1080.hs1', '1080.hu1', '1080.hv1', '1080.hx1', '1440.cx1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [19203926520, 143975, 87182201788, 87657516984, 374659446987, 80787], 'label': '77760.bo.360.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '360.fp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.fp1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246057456
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bu1', '180.bp1', '180.dv1', '180.et1'], 'contains': ['720.eg1', '1080.hs1', '1080.hv1', '1080.hw1', '1440.cy1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [262972240587, 355938186480, 87182202116, 374659084948, 80880, 80787], 'label': '77760.bo.360.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.k1', 'old_label': '360.fq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.fq1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057457
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.bu1', '180.bq1', '180.df1', '180.dn1', '180.dw1', '180.eu1'], 'contains': ['720.du1', '720.dx1', '720.eh1', '1080.hs1', '1080.ht1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [355938284280, 143975, 87182201788, 374659447224, 80880, 80787], 'label': '77760.bo.360.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.fr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.fr1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057458
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.bu1', '180.co1', '180.dx1', '180.ec1'], 'contains': ['720.ei1', '1080.ht1', '1080.hu1', '1080.hw1', '1080.hy1', '1440.da1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [374659447084, 87182201544, 19203926667, 87657516984, 80787, 179159], 'label': '77760.bo.360.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '360.fs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.fs1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057459
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.bu1', '180.dy1'], 'contains': ['720.ej1', '1080.ht1', '1080.hv1', '1080.hw1', '1440.db1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [262972240587, 374659447084, 355938105600, 87182202116, 80787, 179159], 'label': '77760.bo.360.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.dy1', 'old_label': '360.ft1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ft1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 246057460
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.cc1', '180.br1', '180.df1', '180.ed1', '180.ew1', '180.ex1'], 'contains': ['720.dw1', '720.eh1', '1080.hz1', '1080.ia1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [355938186480, 143975, 87182201788, 374659447224, 80880, 80787], 'label': '77760.bo.360.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '360.fu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.fu1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057461
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bv1', '180.a1', '180.m1', '180.cg1'], 'contains': ['720.ek1', '720.eo1', '720.ew1', '1080.ib1', '3240.ek1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [93449082115, 456053207518, 83462998, 174400128000, 224515, 180587232000], 'label': '77760.bo.360.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '360.fv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.fv1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057462
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.s1', '120.bw1', '180.b1', '180.m1', '180.cm1'], 'contains': ['720.ek1', '720.et1', '1080.ic1', '3240.es1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [93449082115, 83601118, 456053207518, 174400128000, 224515, 180587232000], 'label': '77760.bo.360.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '360.fw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.fw1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246057463
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bv1', '120.bx1', '180.g1', '180.n1', '180.bz1'], 'contains': ['720.el1', '720.en1', '720.es1', '1080.ib1', '3240.eu1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [174400208787, 83543730, 93448938387, 456053154955, 180587232000, 80787], 'label': '77760.bo.360.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '360.fx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.fx1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057464
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': ['19440.y2', '19440.j2', '19440.x2', '19440.k2', '19440.x1', '19440.k1', '19440.y1', '19440.j1', '19440.a1', '19440.h1', '19440.f1', '19440.c1'], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.b1', '2.c1'], 'contains': ['8.a1', '12.a1', '12.d1', '24.b1', '40.d1', '60.l1'], 'core': '4.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [87182277125, 143975, 85805, 274511507904, 80880, 80787], 'label': '77760.bo.4.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1', '2.c1'], 'normal_contains': ['8.a1', '12.a1', '1440.a1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '77760.bo', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '77760.bo'}
  • id: 246057465
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '30.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['15.a1'], 'contains': ['60.u1', '60.x1', '60.y1', '60.ba1', '60.bg1', '90.z1', '90.bh1', '120.bc1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [143975, 80787, 262496586694, 143304, 19678982548, 448908283914, 462320323320, 80880, 461841004948], 'label': '77760.bo.30.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '30.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.i1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246057466
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bx1', '180.c1', '180.f1', '180.cg1'], 'contains': ['720.em1', '720.eo1', '720.ev1', '1080.ib1', '3240.ew1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [93449082115, 83548555, 456053069398, 174400128000, 224515, 180587232000], 'label': '77760.bo.360.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '360.fy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.fy1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057467
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.by1', '180.a1', '180.f1', '180.cm1'], 'contains': ['720.ek1', '720.em1', '720.eu1', '1080.id1', '3240.fm1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [93449082115, 83601118, 456053154955, 174400128000, 224515, 180587232000], 'label': '77760.bo.360.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '360.fz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.fz1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057468
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.t1', '120.bw1', '120.bz1', '180.h1', '180.n1', '180.cb1'], 'contains': ['720.el1', '720.eq1', '1080.ic1', '3240.fo1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [174400208787, 93448938387, 456053073961, 180587232000, 80787, 83467561], 'label': '77760.bo.360.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '360.ga1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ga1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057469
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.by1', '180.g1', '180.cb1'], 'contains': ['720.el1', '720.er1', '1080.id1', '3240.fp1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [83548555, 174400208787, 93448938387, 456053073961, 180587232000, 80787], 'label': '77760.bo.360.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '360.gb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.gb1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057470
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.u1', '120.bz1', '180.c1', '180.i1', '180.cm1'], 'contains': ['720.em1', '720.et1', '1080.ic1', '3240.fq1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [180587232243, 93448857748, 456053073961, 148, 174400128148, 83467561], 'label': '77760.bo.360.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '360.gc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.gc1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057471
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.v1', '120.ca1', '120.cb1', '180.n1', '180.ca1'], 'contains': ['720.en1', '720.eq1', '1080.ie1', '3240.fw1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [174400208787, 83543730, 93448938387, 456053150130, 180587232000, 80787], 'label': '77760.bo.360.gd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '360.gd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.gd1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 246057472
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.w1', '120.ca1', '180.c1', '180.m1', '180.ch1'], 'contains': ['720.eo1', '720.et1', '1080.ie1', '3240.gh1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [93449082115, 456053069398, 83462998, 174400128000, 224515, 180587232000], 'label': '77760.bo.360.ge1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '360.ge1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ge1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057473
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.x1', '120.cb1', '180.ci1'], 'contains': ['720.ep1', '720.ex1', '1080.ie1', '3240.gi1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [456053069398, 83462998, 174400128000, 93449036759, 180587232000, 179159], 'label': '77760.bo.360.gf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.s1', 'old_label': '360.gf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.gf1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057474
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.a1', '120.cc1', '180.o1', '180.bs1', '180.cn1', '180.ee1', '180.ey1', '180.ez1', '180.fa1'], 'contains': ['720.ef1', '1080.hz1', '1080.if1', '1080.ig1', '1440.bf1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [355938186480, 262971878400, 374659084948, 80880, 80787, 87182000787], 'label': '77760.bo.360.gg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '360.gg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.gg1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 246057475
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '360.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.g1', '120.cc1', '180.co1', '180.ef1', '180.fb1'], 'contains': ['720.ei1', '1080.ia1', '1080.if1', '1080.ih1', '1440.bg1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [87657292800, 374659447084, 87182201544, 19203926667, 80787, 179159], 'label': '77760.bo.360.gh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.k1', 'old_label': '360.gh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.gh1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057476
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '30.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['15.a1'], 'contains': ['60.v1', '60.w1', '60.y1', '60.bc1', '60.bf1', '90.ba1', '90.bf1', '120.bd1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [87661140722, 355462911480, 143975, 375138270474, 482768881, 80880, 80787, 462320328386, 143304], 'label': '77760.bo.30.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '30.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.j1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246057477
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '405.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['27.a1', '135.a1', '135.b1'], 'contains': ['810.e1', '810.g1', '810.i1', '810.k1', '810.l1', '810.m1', '810.n1', '810.bo1', '810.bq1', '810.bs1', '810.bu1', '1215.a1', '1620.ba1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [262496868215, 362615, 461841045385, 19678982400, 40585, 448908284158, 462320046985], 'label': '77760.bo.405.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1', 'old_label': '405.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '405.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 246057478
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '405.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.b2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['135.a1', '135.c1'], 'contains': ['810.a1', '810.b1', '810.c1', '810.d1', '810.h1', '810.j1', '810.o1', '810.q1', '810.s1', '810.u1', '810.x1', '810.y1', '810.ba1', '810.bb1', '810.bc1', '810.bd1', '810.be1', '810.bv1', '810.bw1', '810.bx1', '810.by1', '810.bz1', '810.cb1', '1215.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [179012, 178680, 19678982400, 5309, 448908284158, 461841010109, 462320328485], 'label': '77760.bo.405.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.b1', 'old_label': '405.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '405.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246057479
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '405.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.m2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['135.b1', '135.c1'], 'contains': ['810.p1', '810.r1', '810.t1', '810.v1', '810.w1', '810.z1', '810.bf1', '810.bg1', '810.bh1', '810.bi1', '810.bj1', '810.bk1', '810.bl1', '810.bm1', '810.bn1', '810.br1', '810.bt1', '1215.a1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [282215, 461841090505, 19679028004, 5309, 448908284158, 462320046842, 80787], 'label': '77760.bo.405.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.c1', 'old_label': '405.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '405.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246057480
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '432.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.b1', '144.a1', '216.c1', '216.d1', '216.i1'], 'contains': ['864.a1', '864.e1', '864.g1', '1296.a1', '1296.c1', '2160.u1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1037836800, 5309, 143975, 80787, 18764565242], 'label': '77760.bo.432.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '432.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 246057481
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '432.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.b1', '216.i1'], 'contains': ['864.a1', '864.h1', '864.i1', '1296.b1', '1296.f1', '2160.be1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1037980104, 143975, 85805, 18764529866, 80787], 'label': '77760.bo.432.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '432.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.b1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 246057482
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '432.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.e1', '144.a1', '216.g1', '216.h1', '216.i1'], 'contains': ['864.b1', '864.e1', '864.h1', '1296.c1', '1296.d1', '2160.bk1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1037836800, 85805, 80880, 80787, 18764565242], 'label': '77760.bo.432.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '432.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.c1', 'subgroup_fusion': None, 'weyl_group': '2160.cr'}
  • id: 246057483
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '432.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.b1', '216.i1'], 'contains': ['864.b1', '864.g1', '864.i1', '1296.e1', '1296.f1', '2160.bm1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1037980104, 85805, 80880, 80787, 18764565242], 'label': '77760.bo.432.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '432.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.d1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 246057484
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '432.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.c1', '216.i1'], 'contains': ['864.a1', '864.b1', '864.c1', '1296.g1', '1296.h1', '2160.bn1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [143975, 85805, 80787, 18764663042, 143304], 'label': '77760.bo.432.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '432.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.e1', 'subgroup_fusion': None, 'weyl_group': '144.143'}
  • id: 246057485
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '432.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.g1', '144.d1', '216.i1', '216.k1', '216.l1'], 'contains': ['864.c1', '864.e1', '864.i1', '1296.i1', '1296.k1', '2160.cj1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1037980104, 18764748747, 80880, 80787, 143304], 'label': '77760.bo.432.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '432.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.f1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 246057486
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '432.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1', '144.d1', '216.m1'], 'contains': ['864.d1', '864.f1', '864.j1', '1296.i1', '1296.l1', '2160.ck1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1037980104, 18764703627, 80787, 143304, 179159], 'label': '77760.bo.432.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.m1', 'old_label': '432.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.g1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246057487
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '30.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.d1', '15.a1'], 'contains': ['60.u1', '60.v1', '60.z1', '60.bb1', '60.bd1', '60.be1', '60.bj1', '90.bb1', '90.bc1', '90.bi1', '120.be1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [143975, 80787, 87661145547, 143304, 462320323320, 80880, 355462911480, 482808988, 375138230375], 'label': '77760.bo.30.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '30.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.k1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
  • id: 246057488
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '432.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.e1', '216.i1'], 'contains': ['864.c1', '864.g1', '864.h1', '1296.j1', '1296.m1', '2160.cr1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [18764748747, 178680, 143975, 1038020645, 80787], 'label': '77760.bo.432.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '432.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.h1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 246057489
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '432.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.k1', '144.f1', '216.c1', '216.g1', '216.k1'], 'contains': ['864.e1', '1296.n1', '1296.q1', '2160.ej1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [181146211175, 269202707012, 143975, 267842044920, 80787], 'label': '77760.bo.432.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '432.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.i1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 246057490
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '432.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.m1', '144.g1', '216.c1', '216.h1', '216.l1'], 'contains': ['864.e1', '1296.o1', '1296.r1', '2160.eo1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [269202707012, 143975, 267842044920, 181146251274, 80787], 'label': '77760.bo.432.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '432.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.j1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 246057491
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '432.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.n1', '144.g1', '216.d1', '216.g1', '216.l1'], 'contains': ['864.e1', '1296.o1', '1296.s1', '2160.ep1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [181146153005, 267841773504, 269202608787, 80880, 80787], 'label': '77760.bo.432.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '432.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.k1', 'subgroup_fusion': None, 'weyl_group': '2160.cr'}
  • id: 246057492
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '432.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.o1', '144.h1', '216.d1', '216.h1', '216.k1'], 'contains': ['864.e1', '1296.p1', '1296.t1', '2160.eq1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [181146067893, 269202707012, 143975, 267842044920, 80787], 'label': '77760.bo.432.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '432.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.l1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 246057493
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '432.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.l1', '144.f1', '216.m1'], 'contains': ['864.f1', '1296.n1', '1296.u1', '2160.er1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [181146291812, 269202671731, 267842045067, 80787, 179159], 'label': '77760.bo.432.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1', 'old_label': '432.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.m1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246057494
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '432.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.p1', '144.h1', '216.m1'], 'contains': ['864.f1', '1296.p1', '1296.v1', '2160.eu1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [181146067893, 269202671731, 267842045067, 80787, 179159], 'label': '77760.bo.432.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.m1', 'old_label': '432.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.n1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 246057495
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '432.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.a1', '144.i1', '144.j1', '216.e1', '216.j1', '216.p1', '216.t1', '216.v1'], 'contains': ['1296.w1', '2160.fd1', '2592.g1', '4320.bj1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25470592804, 286482919204, 80787], 'label': '77760.bo.432.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '432.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.o1', 'subgroup_fusion': None, 'weyl_group': '240.189'}
  • id: 246057496
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '432.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.q1', '144.i1', '216.b1', '216.f1', '216.n1', '216.q1', '216.s1', '216.u1', '216.w1'], 'contains': ['1296.w1', '2160.fg1', '2592.h1', '4320.bk1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [455574211175, 349232083200, 143975], 'label': '77760.bo.432.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '432.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.p1', 'subgroup_fusion': None, 'weyl_group': '240.189'}
  • id: 246057497
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '432.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.r1', '144.j1', '216.o1', '216.r1', '216.x1'], 'contains': ['1296.w1', '2160.fi1', '2592.i1', '4320.bl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [286483052759, 25470726359, 179159], 'label': '77760.bo.432.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.m1', 'old_label': '432.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.q1', 'subgroup_fusion': None, 'weyl_group': '240.189'}
  • id: 246057498
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '30.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.e1', '15.a1'], 'contains': ['60.w1', '60.x1', '60.z1', '60.bh1', '60.bi1', '90.bd1', '90.bj1', '120.bf1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [143975, 80787, 143304, 375138270474, 87661140722, 80880, 355462911480, 482808988, 462320328386], 'label': '77760.bo.30.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '30.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.l1', 'subgroup_fusion': None, 'weyl_group': '2592.lc'}
  • id: 246057499
    {'ambient': '77760.bo', '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': '2880.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['160.a1', '240.a1', '240.b1', '240.c1', '240.d1', '240.r1'], 'contains': ['960.b1', '1440.c1', '1440.d1', '1440.e1', '1440.f1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [183845, 280259700485, 80880, 80787, 193999357587], 'label': '77760.bo.480.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '480.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 246057500
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.m1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['160.a1', '240.f1', '240.k1', '240.o1'], 'contains': ['960.a1', '1440.e1', '1440.h1', '1440.i1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 160, 'diagramx': None, 'generators': [183845, 143975, 280259700485, 193999455812, 80787], 'label': '77760.bo.480.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.a1', 'old_label': '480.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.b1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057501
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['160.a1', '240.g1', '240.j1', '240.l1', '240.p1', '240.r1'], 'contains': ['960.b1', '1440.f1', '1440.g1', '1440.h1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [280259521949, 85805, 80880, 80787, 193999357587], 'label': '77760.bo.480.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '480.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.c1', 'subgroup_fusion': None, 'weyl_group': '864.2470'}
  • id: 246057502
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.m1', '160.a1', '240.e1', '240.h1', '240.i1', '240.m1', '240.n1', '240.q1', '240.s1'], 'contains': ['960.c1', '1440.a1', '1440.d1', '1440.h1', '1440.i1'], 'core': '1440.a1', 'coset_action_label': None, 'count': 80, 'diagramx': None, 'generators': [183845, 194518374451, 143975, 80880, 80787], 'label': '77760.bo.480.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '480.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.d1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057503
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['160.b1', '240.r1', '240.t1', '240.v1', '240.x1', '240.y1'], 'contains': ['960.b1', '1440.j1', '1440.k1', '1440.m1', '1440.n1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [193999357894, 280259527104, 80880, 80787, 693], 'label': '77760.bo.480.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '480.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.e1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 246057504
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.b1', '240.u1', '240.w1'], 'contains': ['960.e1', '1440.j1', '1440.l1', '1440.o1', '1440.p1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [193999357894, 280259481600, 224184, 80787, 179159], 'label': '77760.bo.480.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.s1', 'old_label': '480.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.f1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 246057505
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.bg1', '160.b1', '240.s1', '240.z1', '240.ba1', '240.bb1', '240.bc1', '240.bd1', '240.be1'], 'contains': ['960.c1', '1440.b1', '1440.k1', '1440.l1'], 'core': '1440.b1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [355419504452, 143975, 80880, 80787, 143304], 'label': '77760.bo.480.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '480.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.g1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057506
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.bh1', '160.c1', '240.e1', '240.z1', '240.bf1', '240.bg1', '240.bq1'], 'contains': ['960.c1', '1440.q1', '1440.r1', '1440.s1', '1440.t1', '1440.u1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [143975, 174436416243, 80880, 80787, 375138230375], 'label': '77760.bo.480.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '480.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.h1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057507
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['160.c1', '240.f1', '240.bh1', '240.bl1'], 'contains': ['960.a1', '1440.r1', '1440.v1', '1440.x1', '1440.y1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 160, 'diagramx': None, 'generators': [93449001331, 83606375, 143975, 174400128243, 80787], 'label': '77760.bo.480.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.a1', 'old_label': '480.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.i1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057508
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['160.c1', '240.a1', '240.g1', '240.t1', '240.bi1', '240.bk1', '240.bm1', '240.br1'], 'contains': ['960.b1', '1440.q1', '1440.v1', '1440.x1', '1440.z1', '1440.ba1', '1440.bb1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 80, 'diagramx': None, 'generators': [174400208787, 93449036612, 83606375, 143975, 80787], 'label': '77760.bo.480.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '480.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.j1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057509
    {'ambient': '77760.bo', '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': '1440.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.b1', '12.l1', '18.c1', '18.j1'], 'contains': ['72.a1', '108.a1', '216.p1', '360.dw1', '540.ga1'], 'core': '36.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [93924311187, 462320052004, 80787], 'label': '77760.bo.36.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': ['12.b1'], 'normal_contains': ['72.a1', '108.a1'], 'normalizer': '1.a1', 'old_label': '36.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1', 'subgroup_fusion': None, 'weyl_group': '1440.5842'}
  • id: 246057510
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.bi1', '160.c1', '240.h1', '240.ba1', '240.bj1', '240.bn1', '240.bq1'], 'contains': ['960.c1', '1440.s1', '1440.v1', '1440.w1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [143975, 188331136563, 80880, 80787, 375138230375], 'label': '77760.bo.480.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '480.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.k1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057511
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['160.c1', '240.bo1'], 'contains': ['960.d1', '1440.u1', '1440.w1', '1440.x1', '1440.y1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 160, 'diagramx': None, 'generators': [83687012, 174400128243, 93449081975, 80787, 179159], 'label': '77760.bo.480.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '80.k1', 'old_label': '480.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.l1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 246057512
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['160.c1', '240.u1', '240.bp1', '240.bs1'], 'contains': ['960.e1', '1440.t1', '1440.w1', '1440.y1', '1440.z1', '1440.bc1', '1440.bd1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 80, 'diagramx': None, 'generators': [174400208787, 93449001331, 83687012, 80787, 179159], 'label': '77760.bo.480.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.i1', 'old_label': '480.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.m1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057513
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.a1', '120.cc1', '160.d1', '240.i1', '240.bb1', '240.bq1', '240.bt1', '240.bu1'], 'contains': ['960.c1', '1440.be1', '1440.bf1', '1440.bg1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [143975, 88176390359, 80880, 80787, 113567005680], 'label': '77760.bo.480.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '480.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.n1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057514
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['160.d1', '240.b1', '240.j1', '240.v1', '240.br1', '240.bw1', '240.bx1', '240.by1', '240.ca1', '240.cb1', '240.cc1', '240.cd1'], 'contains': ['960.b1', '1440.bf1', '1440.bh1', '1440.bi1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [482711044, 280259527104, 80880, 80787, 193999357587], 'label': '77760.bo.480.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '480.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.o1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 246057515
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.d1', '240.w1', '240.bs1', '240.bz1', '240.ce1', '240.cf1'], 'contains': ['960.e1', '1440.bg1', '1440.bh1', '1440.bj1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [280259481600, 482676004, 193999420531, 80787, 179159], 'label': '77760.bo.480.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.g1', 'old_label': '480.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.p1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057516
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['160.e1', '240.k1', '240.bh1', '240.cl1'], 'contains': ['960.a1', '1440.bk1', '1440.bp1', '1440.bs1', '1440.bv1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [83601118, 93449001331, 143975, 174400173363, 80787], 'label': '77760.bo.480.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.g1', 'old_label': '480.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.q1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057517
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['160.e1', '240.a1', '240.l1', '240.x1', '240.bi1', '240.bw1', '240.cg1', '240.cm1'], 'contains': ['960.b1', '1440.bk1', '1440.bl1', '1440.bm1', '1440.bn1', '1440.bt1', '1440.bu1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [456053074316, 93448857748, 174400173363, 80880, 80787], 'label': '77760.bo.480.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '480.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.r1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057518
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.n1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bp1', '160.e1', '240.e1', '240.m1', '240.bc1', '240.bj1', '240.bt1', '240.ch1', '240.cn1'], 'contains': ['960.c1', '1440.bk1', '1440.bo1', '1440.bq1', '1440.br1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [442641300482, 143975, 519235320, 80880, 80787], 'label': '77760.bo.480.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '480.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.s1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057519
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['160.e1', '240.f1', '240.ci1', '240.cl1'], 'contains': ['960.a1', '1440.bq1', '1440.bt1', '1440.bv1', '1440.by1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 160, 'diagramx': None, 'generators': [174400208787, 93449001331, 456053154955, 143975, 80787], 'label': '77760.bo.480.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.a1', 'old_label': '480.t1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.t1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057520
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '18.a1', '18.b1', '18.g1'], 'contains': ['72.q1', '108.d1', '216.b1', '360.d1', '540.i1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87182277125, 274511462400, 143975, 5066], 'label': '77760.bo.36.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1', 'subgroup_fusion': None, 'weyl_group': '1440.5842'}
  • id: 246057521
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['160.e1', '240.c1', '240.g1', '240.x1', '240.bk1', '240.bx1', '240.cj1', '240.cm1'], 'contains': ['960.b1', '1440.bo1', '1440.bs1', '1440.bu1', '1440.bw1', '1440.bx1', '1440.by1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 80, 'diagramx': None, 'generators': [93448857748, 174400173363, 456053073961, 80880, 80787], 'label': '77760.bo.480.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '480.u1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.u1', 'subgroup_fusion': None, 'weyl_group': '1296.2985'}
  • id: 246057522
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bq1', '160.e1', '240.h1', '240.n1', '240.bd1', '240.bf1', '240.bt1', '240.ck1', '240.cn1'], 'contains': ['960.c1', '1440.bn1', '1440.bp1', '1440.br1', '1440.by1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 80, 'diagramx': None, 'generators': [143975, 188331136563, 375138172555, 80880, 80787], 'label': '77760.bo.480.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '480.v1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.v1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057523
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['160.f1', '240.k1', '240.bl1', '240.ci1'], 'contains': ['960.a1', '1440.bz1', '1440.cb1', '1440.cc1', '1440.cf1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [174400352612, 93448857748, 456053150130, 80880, 80787], 'label': '77760.bo.480.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.g1', 'old_label': '480.w1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.w1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057524
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['160.f1', '240.c1', '240.l1', '240.t1', '240.bm1', '240.by1', '240.cg1', '240.cj1'], 'contains': ['960.b1', '1440.bz1', '1440.cb1', '1440.cd1', '1440.ce1', '1440.cj1', '1440.ck1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [93448857748, 83543730, 174400173363, 80880, 80787], 'label': '77760.bo.480.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.m1', 'old_label': '480.x1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.x1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057525
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.br1', '160.f1', '240.m1', '240.z1', '240.bn1', '240.bu1', '240.ck1'], 'contains': ['960.c1', '1440.bz1', '1440.ca1', '1440.cg1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [442641386755, 143975, 519235320, 80880, 80787], 'label': '77760.bo.480.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '480.y1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.y1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057526
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['160.f1', '240.bo1'], 'contains': ['960.d1', '1440.ca1', '1440.cb1', '1440.cc1', '1440.ci1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [93449001331, 174400173363, 456053150130, 80787, 179159], 'label': '77760.bo.480.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.bo1', 'old_label': '480.z1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.z1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 246057527
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['160.f1', '240.u1', '240.bp1', '240.bz1'], 'contains': ['960.e1', '1440.ca1', '1440.cc1', '1440.cd1', '1440.ch1', '1440.cl1', '1440.cm1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [174400208787, 93449001331, 456053150130, 80787, 179159], 'label': '77760.bo.480.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.x1', 'old_label': '480.ba1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.ba1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057528
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.bs1', '160.f1', '240.n1', '240.ba1', '240.bg1', '240.bu1', '240.ch1'], 'contains': ['960.c1', '1440.ce1', '1440.cf1', '1440.cg1', '1440.ch1', '1440.ci1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [375138087093, 143975, 188331136563, 80880, 80787], 'label': '77760.bo.480.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1', 'old_label': '480.bb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.bb1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057529
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['160.g1', '240.o1', '240.bh1', '240.ci1'], 'contains': ['960.a1', '1440.cn1', '1440.co1', '1440.ct1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [193999455812, 280259527104, 482768881, 80880, 80787], 'label': '77760.bo.480.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.g1', 'old_label': '480.bc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.bc1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057530
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['160.g1', '240.b1', '240.p1', '240.y1', '240.bi1', '240.cj1'], 'contains': ['960.b1', '1440.cn1', '1440.cq1', '1440.cr1', '1440.cu1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [280259481600, 482635561, 143975, 193999455812, 80787], 'label': '77760.bo.480.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '480.bd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.bd1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 246057531
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.b1', '12.e1', '18.i1'], 'contains': ['72.b1', '72.k1', '72.m1', '108.b1', '108.e1', '180.e1', '216.c1', '360.k1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [479363787, 443555838725, 143975, 85805, 80787], 'label': '77760.bo.36.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '36.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1', 'subgroup_fusion': None, 'weyl_group': '1440.5849'}
  • id: 246057532
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['120.bt1', '160.g1', '240.i1', '240.q1', '240.be1', '240.bf1', '240.bj1', '240.ch1', '240.ck1'], 'contains': ['960.c1', '1440.cn1', '1440.co1', '1440.cp1', '1440.cs1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 240, 'diagramx': None, 'generators': [88176350010, 143975, 80880, 80787, 113567005680], 'label': '77760.bo.480.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '480.be1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.be1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057533
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['160.g1', '240.d1', '240.j1', '240.y1', '240.bk1', '240.cg1'], 'contains': ['960.b1', '1440.cs1', '1440.ct1', '1440.cu1', '1440.cv1', '1440.cw1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [482635561, 280259527104, 80880, 80787, 193999357587], 'label': '77760.bo.480.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '480.bf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.bf1', 'subgroup_fusion': None, 'weyl_group': '7776.is'}
  • id: 246057534
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['160.h1', '240.o1', '240.bl1', '240.cl1'], 'contains': ['960.a1', '1440.cx1', '1440.cy1', '1440.dc1', '1440.dd1', '1440.df1', '1440.df2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [482808988, 280259705975, 193999455812, 80880, 80787], 'label': '77760.bo.480.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.g1', 'old_label': '480.bg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.bg1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057535
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['160.h1', '240.d1', '240.p1', '240.v1', '240.bm1', '240.cm1'], 'contains': ['960.b1', '1440.cx1', '1440.dc1', '1440.de1', '1440.dg1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [482808988, 280259481600, 143975, 193999455812, 80787], 'label': '77760.bo.480.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1', 'old_label': '480.bh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.bh1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 246057536
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['120.bu1', '160.h1', '240.q1', '240.bb1', '240.bg1', '240.bn1', '240.cn1'], 'contains': ['960.c1', '1440.cx1', '1440.cy1', '1440.cz1', '1440.da1', '1440.db1'], 'core': '2880.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [88176292437, 143975, 80880, 80787, 113567005680], 'label': '77760.bo.480.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.o1', 'old_label': '480.bi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.bi1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057537
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['160.h1', '240.bo1'], 'contains': ['960.d1', '1440.da1', '1440.db1', '1440.dc1', '1440.dd1', '1440.df1', '1440.df2'], 'core': '25920.a1', 'coset_action_label': None, 'count': 480, 'diagramx': None, 'generators': [482808988, 193999455812, 280259527104, 80787, 179159], 'label': '77760.bo.480.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.bo1', 'old_label': '480.bj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.bj1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 246057538
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '480.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.h1', '240.w1', '240.bp1'], 'contains': ['960.e1', '1440.da1', '1440.dd1', '1440.de1', '1440.dh1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [482808988, 280259481600, 193999420531, 80787, 179159], 'label': '77760.bo.480.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.s1', 'old_label': '480.bk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.bk1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 246057539
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.d1', '270.a1', '270.c1', '270.u1'], 'contains': ['1080.h1', '1080.ej1', '1080.gi1', '1620.h1', '1620.i1', '1620.j1', '2160.a1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [355462738109, 375138270718, 179012, 87660926909, 5309, 462320328485], 'label': '77760.bo.540.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.a1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246057540
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.b1', '180.e1', '270.b1', '270.c1', '270.v1'], 'contains': ['1080.h1', '1080.eo1', '1080.gk1', '1620.f1', '1620.k1', '2160.b1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [443120250115, 180667151546, 442162022400, 224515, 85946, 442641305788], 'label': '77760.bo.540.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.b1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.b1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246057541
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.a1', '180.f1', '180.g1', '270.e1'], 'contains': ['1080.f1', '1080.i1', '1080.k1', '1080.eq1', '1080.er1', '1080.ib1', '1080.id1', '4860.d1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [456053154955, 174400128000, 85805, 83462400, 180587232000, 93448857600], 'label': '77760.bo.540.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.e1', 'old_label': '540.c1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.c1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246057542
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.c1', '12.f1', '18.i1'], 'contains': ['72.b1', '72.n1', '72.o1', '108.c1', '108.h1', '180.k1', '216.d1', '360.n1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [174879492452, 277050, 80880, 80787, 462320046985], 'label': '77760.bo.36.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '36.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1', 'subgroup_fusion': None, 'weyl_group': '4320.bp'}
  • id: 246057543
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.a1', '180.b1', '180.h1', '180.i1', '270.e1'], 'contains': ['1080.f1', '1080.j1', '1080.eq1', '1080.es1', '1080.ic1', '4860.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [5161, 174400128000, 456053073961, 83462400, 180587232000, 93448857600], 'label': '77760.bo.540.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1', 'old_label': '540.d1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.d1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246057544
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.j1', '270.b1', '270.d1', '270.u1'], 'contains': ['1080.h1', '1080.gp1', '1080.he1', '1620.q1', '1620.u1', '2160.g1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [355462738109, 179012, 87661105445, 5309, 375138092159, 462320328958], 'label': '77760.bo.540.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.e1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057545
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.c1', '180.k1', '270.a1', '270.d1', '270.v1'], 'contains': ['1080.h1', '1080.gt1', '1080.hi1', '1620.r1', '1620.s1', '1620.t1', '2160.j1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [179012, 443120204612, 442162022400, 442641341252, 180667106042, 40442], 'label': '77760.bo.540.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.f1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057546
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.l1', '270.a1', '270.b1', '270.w1'], 'contains': ['1080.h1', '1080.hq1', '1080.hx1', '1620.v1', '1620.w1', '1620.x1', '2160.k1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87182277597, 262972235525, 143975, 374659441925, 355938110666, 5066], 'label': '77760.bo.540.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.g1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057547
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.b1', '180.c1', '180.m1', '180.n1', '270.e1'], 'contains': ['1080.i1', '1080.j1', '1080.ib1', '1080.ic1', '1080.ie1', '4860.l1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [83462998, 456053154955, 174400128000, 85946, 180587232000, 93448857600], 'label': '77760.bo.540.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.e1', 'old_label': '540.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.h1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246057548
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.b1', '180.o1', '270.c1', '270.d1', '270.w1'], 'contains': ['1080.h1', '1080.hl1', '1080.ig1', '1620.y1', '1620.z1', '2160.e1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [262972235525, 87182277125, 143975, 374659441925, 355938110666, 5066], 'label': '77760.bo.540.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.i1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246057549
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.p1', '180.r1', '270.e1'], 'contains': ['1080.d1', '1080.f1', '1080.i1', '1080.l1', '1080.m1', '1080.cc1', '1080.ce1', '1080.ch1', '1620.ba1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [40349, 83462998, 598, 174400128000, 180587232000, 93448857600], 'label': '77760.bo.540.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.e1', 'old_label': '540.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.j1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246057550
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1', '180.q1', '180.s1', '270.e1'], 'contains': ['1080.j1', '1080.k1', '1080.m1', '1080.ci1', '1080.cj1', '4860.t1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [482849425, 40585, 280259522185, 88695348625, 193999420104, 143304], 'label': '77760.bo.540.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.e1', 'old_label': '540.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.k1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246057551
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dp1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.t1', '270.f1', '270.o1', '270.bg1'], 'contains': ['1080.r2', '1080.x1', '1080.y1', '1080.du1', '1080.dw1', '1080.ey1', '1080.ez1', '1620.a1', '1620.bc1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [143975, 80787, 462320328485, 7185029309, 19679028004, 5309], 'label': '77760.bo.540.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.l1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246057552
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.u1', '270.j1', '270.bg1'], 'contains': ['1080.r2', '1080.z1', '1080.ba1', '1080.dv1', '1080.dx1', '1080.fa1', '1080.fb1', '1620.b1', '1620.bd1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [7185207845, 19679028004, 143975, 85805, 80787, 462320328386], 'label': '77760.bo.540.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.m1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057553
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '12.d1', '18.c1', '18.f1', '18.h1'], 'contains': ['72.a1', '108.d1', '216.e1', '360.r1', '540.bp1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [87181925066, 274511462400, 85805, 80787], 'label': '77760.bo.36.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.e1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
  • id: 246057554
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.v1', '270.h1', '270.j1', '270.bh1'], 'contains': ['1080.r1', '1080.ba1', '1080.bb1', '1080.dr1', '1080.ds1', '1080.ew1', '1080.ex1', '1620.c1', '1620.bh1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87182277125, 482849425, 143975, 375138270474, 85805, 80787], 'label': '77760.bo.540.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.n1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057555
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.a1', '180.w1', '270.g1', '270.j1', '270.bi1'], 'contains': ['1080.r1', '1080.w1', '1080.z1', '1080.dl1', '1080.do1', '1080.eu1', '1080.fn1', '1620.d1', '1620.bk1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [183845, 87261834480, 83543044, 456053073961, 80880, 80787], 'label': '77760.bo.540.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.o1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057556
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.x1', '270.f1', '270.j1', '270.bj1'], 'contains': ['1080.o1', '1080.o2', '1080.r2', '1080.w1', '1080.bb1', '1080.dh1', '1080.dh3', '1080.dk1', '1080.dm1', '1080.et1', '1080.fm1', '1620.e1', '1620.bl1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841223825, 19679028004, 143975, 85805, 80787, 462320328386], 'label': '77760.bo.540.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.p1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057557
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.p2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.x2', '270.g1', '270.h1', '270.bj1'], 'contains': ['1080.o1', '1080.o2', '1080.r1', '1080.w2', '1080.bb1', '1080.dh2', '1080.dh4', '1080.dk2', '1080.dm2', '1080.et2', '1080.fm2', '1620.e2', '1620.bl2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841223825, 19679028004, 143975, 462320328958, 85805, 80787], 'label': '77760.bo.540.p2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.p2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.p2', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057558
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.ce2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.e1', '180.y1', '270.g1', '270.o1', '270.bh1'], 'contains': ['1080.r1', '1080.x1', '1080.be1', '1080.dq1', '1080.ea1', '1080.ev1', '1080.gj1', '1620.f1', '1620.bm1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [443120071204, 183845, 442641024148, 180667249346, 80880, 80787], 'label': '77760.bo.540.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.q1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.q1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246057559
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.ce2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.b1', '180.z1', '270.h1', '270.o1', '270.bi1'], 'contains': ['1080.r1', '1080.y1', '1080.dj1', '1080.ec1', '1080.fc1', '1620.g1', '1620.bo1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [87261834480, 86155, 456053074316, 83543044, 80880, 80787], 'label': '77760.bo.540.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.r1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.r1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246057560
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.ec1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.d1', '180.bc1', '270.j1', '270.o1', '270.bj1'], 'contains': ['1080.r1', '1080.r2', '1080.be1', '1080.di1', '1080.di2', '1080.ee1', '1080.gm1', '1620.h1', '1620.bq1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [277050, 19678982548, 462320328958, 80880, 80787, 448908283914], 'label': '77760.bo.540.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '540.s1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.s1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057561
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.d1', '180.ba1', '270.k1', '270.p1', '270.x1'], 'contains': ['1080.bf1', '1080.eg1', '1080.gn1', '1620.i1', '1620.bq1', '2160.p1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [355462738109, 87660962042, 5309, 462320046842, 80787, 375138126842], 'label': '77760.bo.540.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '540.t1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.t1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057562
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.d1', '180.bb1', '270.l1'], 'contains': ['1080.bg1', '1080.eh1', '1080.go1', '1620.j1', '1620.bq1', '2160.q1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [355462871610, 87660962042, 5309, 462320046842, 80787, 375138126842], 'label': '77760.bo.540.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1', 'old_label': '540.u1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.u1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057563
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.ba1', '270.i1', '270.q1', '270.u1'], 'contains': ['1080.bh1', '1080.ej1', '1080.gp1', '1620.i1', '1620.br1', '2160.r1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [462320092205, 355462738109, 87660926909, 85805, 375138172205, 80880], 'label': '77760.bo.540.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.v1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.v1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057564
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '18.d1', '18.e1', '18.g1'], 'contains': ['72.q1', '108.d1', '216.f1', '360.t1', '540.bq1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [87181925066, 5066, 274511507904, 80880], 'label': '77760.bo.36.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.f1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
  • id: 246057565
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.e1', '180.e1', '180.bd1', '270.n1', '270.p1', '270.y1'], 'contains': ['1080.bf1', '1080.en1', '1080.gr1', '1620.k1', '1620.bm1', '2160.s1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [188331171987, 87181925066, 85805, 375138172205, 80787, 482670985], 'label': '77760.bo.540.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '540.w1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.w1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057566
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.f1', '180.bd1', '270.m1', '270.q1', '270.v1'], 'contains': ['1080.bh1', '1080.eo1', '1080.gt1', '1620.k1', '1620.bn1', '2160.t1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [442641104880, 443120025600, 180667151546, 442162067904, 5066, 80880], 'label': '77760.bo.540.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.x1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.x1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057567
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.be1', '270.g1', '270.bg1'], 'contains': ['1080.w2', '1080.x1', '1080.z1', '1080.fi1', '1080.fk1', '1080.ft1', '1080.fw1', '1620.l1', '1620.bw1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [7185029309, 19679028004, 5309, 143975, 462320328958, 80787], 'label': '77760.bo.540.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.y1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.y1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057568
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.bf1', '270.h1', '270.r1', '270.bg1'], 'contains': ['1080.w2', '1080.y1', '1080.ba1', '1080.fj1', '1080.fl1', '1080.fu1', '1080.fv1', '1620.m1', '1620.bx1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [7185207845, 19679028004, 143975, 462320328958, 85805, 80787], 'label': '77760.bo.540.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.z1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.z1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057569
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.bg1', '270.f1', '270.g1', '270.bh1'], 'contains': ['1080.w1', '1080.x1', '1080.bb1', '1080.fg1', '1080.fh1', '1080.fq1', '1080.fr1', '1620.n1', '1620.by1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [443120071204, 442641386755, 277050, 180667151546, 80880, 80787], 'label': '77760.bo.540.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.ba1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ba1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057570
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.c1', '180.bh1', '270.f1', '270.r1', '270.bi1'], 'contains': ['1080.w1', '1080.y1', '1080.fe1', '1080.fo1', '1080.fz1', '1620.o1', '1620.bz1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [87261834480, 86155, 83543730, 456053073961, 80880, 80787], 'label': '77760.bo.540.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.bb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bb1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057571
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.bi1', '270.f1', '270.h1', '270.bk1'], 'contains': ['1080.y1', '1080.bb1', '1080.gd1', '1080.gf1', '1080.gg1', '1620.p1', '1620.cb1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [355938289445, 87182277597, 374659361282, 5309, 143975, 80787], 'label': '77760.bo.540.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.bc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bc1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057572
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.bj1', '270.m1', '270.s1', '270.u1'], 'contains': ['1080.bh1', '1080.gi1', '1080.he1', '1620.q1', '1620.cd1', '2160.x1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [375138408958, 355462738109, 87661279434, 45363, 40585, 462320328958], 'label': '77760.bo.540.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.bd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bd1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057573
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.g1', '180.bk1', '270.i1', '270.s1', '270.v1'], 'contains': ['1080.bh1', '1080.gk1', '1080.hi1', '1620.s1', '1620.cc1', '2160.z1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [443120025600, 180667151546, 45363, 40585, 442641341252, 442162103044], 'label': '77760.bo.540.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.be1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.be1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057574
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.j1', '180.bj1', '270.n1', '270.t1', '270.x1'], 'contains': ['1080.bf1', '1080.gn1', '1080.gw1', '1620.q1', '1620.cf1', '2160.y1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87661279197, 355462738109, 375138363450, 5309, 462320328958, 80787], 'label': '77760.bo.540.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '540.bf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bf1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057575
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': ['19440.j1', '19440.x1', '19440.a1', '19440.c1', '19440.j2', '19440.x2'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '2.d1', '2.e1'], 'contains': ['8.a1', '12.h1', '12.i1', '24.c1', '40.k1', '60.z1'], 'core': '4.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [87182202116, 143975, 274511507904, 80880, 80787, 143304], 'label': '77760.bo.4.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': ['2.c1', '2.d1', '2.e1'], 'normal_contains': ['8.a1', '1440.b1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '77760.bo', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '25920.w'}
  • id: 246057576
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.a1', '12.e1', '18.i1'], 'contains': ['72.e1', '72.k1', '72.n1', '108.e1', '108.f1', '180.bd1', '216.g1', '360.be1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [183845, 479363787, 443555839197, 143975, 80787], 'label': '77760.bo.36.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '36.g1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1', 'subgroup_fusion': None, 'weyl_group': '12960.bv'}
  • id: 246057577
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.k1', '180.bm1', '270.j1', '270.r1', '270.bh1'], 'contains': ['1080.w1', '1080.ba1', '1080.be1', '1080.ff1', '1080.fp1', '1080.gq1', '1080.gx1', '1620.r1', '1620.ce1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [443120071204, 442641386755, 277050, 180667342797, 80880, 80787], 'label': '77760.bo.540.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.bg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bg1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057578
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.h1', '180.k1', '180.bk1', '270.k1', '270.t1', '270.y1'], 'contains': ['1080.bf1', '1080.gr1', '1080.gz1', '1620.s1', '1620.ce1', '2160.bb1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [443120071204, 442641386755, 5309, 442162022400, 180667106042, 80787], 'label': '77760.bo.540.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '540.bh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bh1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057579
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.k1', '180.bl1', '270.l1'], 'contains': ['1080.bg1', '1080.gs1', '1080.ha1', '1620.t1', '1620.ce1', '2160.bc1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [87181925066, 188331270212, 85805, 375138172555, 80787, 482670985], 'label': '77760.bo.540.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.l1', 'old_label': '540.bi1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bi1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057580
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.j1', '180.bn1', '270.g1', '270.r1', '270.bj1'], 'contains': ['1080.w1', '1080.w2', '1080.be1', '1080.fd1', '1080.fd2', '1080.gv1', '1080.hc1', '1620.u1', '1620.cf1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841090505, 19679028004, 5309, 143975, 462320328958, 80787], 'label': '77760.bo.540.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '540.bj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bj1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057581
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.bo1', '270.i1', '270.m1', '270.w1'], 'contains': ['1080.bh1', '1080.hl1', '1080.hx1', '1620.w1', '1620.cg1', '2160.bd1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87182277597, 374659170505, 45363, 355938191305, 262971883466, 5066], 'label': '77760.bo.540.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.bk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bk1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057582
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.l1', '180.bq1', '270.g1', '270.j1', '270.bk1'], 'contains': ['1080.z1', '1080.bb1', '1080.be1', '1080.gb1', '1080.ge1', '1080.hn1', '1080.hs1', '1620.v1', '1620.ch1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [355938289445, 374659361521, 87182277125, 143975, 85805, 80787], 'label': '77760.bo.540.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.bl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bl1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057583
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.l1', '180.bo1', '270.k1', '270.n1', '270.z1'], 'contains': ['1080.bf1', '1080.ho1', '1080.hu1', '1620.w1', '1620.ch1', '2160.bf1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87182277597, 355938191405, 374659170605, 85805, 80787, 262971964205], 'label': '77760.bo.540.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '540.bm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bm1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057584
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.l1', '180.bp1', '270.l1'], 'contains': ['1080.bg1', '1080.hp1', '1080.hv1', '1620.x1', '1620.ch1', '2160.bg1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [87182277597, 355938191405, 262972155121, 374659170605, 85805, 80787], 'label': '77760.bo.540.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.l1', 'old_label': '540.bn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bn1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057585
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.ce2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.o1', '180.br1', '270.o1', '270.r1', '270.bk1'], 'contains': ['1080.y1', '1080.be1', '1080.gc1', '1080.hk1', '1080.hz1', '1620.y1', '1620.ci1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [374659361521, 355938191405, 87182277125, 143975, 85805, 80787], 'label': '77760.bo.540.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.bo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bo1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246057586
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.bl1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.e1', '180.o1', '180.bs1', '270.p1', '270.t1', '270.z1'], 'contains': ['1080.bf1', '1080.ho1', '1080.if1', '1620.z1', '1620.ci1', '2160.v1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [87182277597, 277050, 262972155450, 374659361850, 355938382650, 80787], 'label': '77760.bo.540.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '540.bp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bp1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057587
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.d1', '12.f1', '18.i1'], 'contains': ['72.e1', '72.m1', '72.o1', '108.g1', '108.h1', '180.bk1', '216.h1', '360.bl1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [174879492452, 462320328958, 85805, 80880, 80787], 'label': '77760.bo.36.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '36.h1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1', 'subgroup_fusion': None, 'weyl_group': '4320.bp'}
  • id: 246057588
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.f1', '180.bs1', '270.q1', '270.s1', '270.w1'], 'contains': ['1080.bh1', '1080.hq1', '1080.ig1', '1620.z1', '1620.cj1', '2160.w1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [355938146042, 87181925066, 262971883466, 5066, 374659125242, 80880], 'label': '77760.bo.540.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.bq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bq1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057589
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['54.d1', '135.a1', '180.p1', '180.bt1'], 'contains': ['1080.a1', '1080.b1', '1080.e1', '1080.g1', '1080.n1', '1080.s1', '1080.v1', '1080.bc1', '1080.bi1', '1080.bj1', '1080.bk1', '1080.cl1', '1080.cp1', '1080.cq1', '1080.da1', '1620.ba1', '1620.ck1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 2160, 'diagramx': None, 'generators': [997965504, 442641104880, 518918400, 85805, 80880, 143304], 'label': '77760.bo.540.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.br1', 'old_label': '540.br1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.br1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246057590
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.i1', '180.bu1', '270.u1', '270.v1', '270.w1'], 'contains': ['1080.h1', '1080.bh1', '1080.dd1', '1620.bb1', '1620.cn1', '2160.bh1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [362615, 355419504452, 355499106746, 442681298634, 45363, 40585], 'label': '77760.bo.540.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.bs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bs1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057591
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.e1', '135.b1', '180.r1', '180.bt1'], 'contains': ['1080.p1', '1080.t1', '1080.u1', '1080.bd1', '1080.bl1', '1080.bm1', '1080.bn1', '1080.bz1', '1080.ca1', '1080.cd1', '1080.cf1', '1620.ba1', '1620.co1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [518964004, 442641024000, 998000787, 85805, 80787, 143304], 'label': '77760.bo.540.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '540.bt1', 'old_label': '540.bt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bt1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246057592
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.j1', '180.bu1', '270.x1', '270.y1', '270.z1'], 'contains': ['1080.bf1', '1080.cg1', '1620.bb1', '1620.cr1', '2160.bi1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [282215, 355499061242, 355419504452, 5309, 442681217850, 80787], 'label': '77760.bo.540.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '540.bu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bu1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057593
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.t1', '270.ba1', '270.be1', '270.bg1'], 'contains': ['1080.bp2', '1080.br1', '1080.bs1', '1080.du1', '1080.dx1', '1080.fi1', '1080.fj1', '1620.bc1', '1620.be1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [7185029309, 19678982548, 85805, 80880, 80787, 462320046985], 'label': '77760.bo.540.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '540.bv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bv1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 246057594
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.u1', '270.bd1', '270.bg1'], 'contains': ['1080.bp2', '1080.bt1', '1080.bu1', '1080.dv1', '1080.dw1', '1080.fk1', '1080.fl1', '1620.bd1', '1620.bf1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [7185162389, 19678982548, 85805, 80880, 80787, 462320046985], 'label': '77760.bo.540.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.bw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bw1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057595
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.v1', '270.bc1', '270.bd1', '270.bh1'], 'contains': ['1080.bp1', '1080.bu1', '1080.bv1', '1080.dq1', '1080.ds1', '1080.ff1', '1080.fh1', '1620.bg1', '1620.bh1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [80787, 482768881, 87181925066, 375138172205, 85805, 80880], 'label': '77760.bo.540.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.bx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bx1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057596
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.f1', '180.w1', '270.bb1', '270.bd1', '270.bi1'], 'contains': ['1080.bp1', '1080.bq1', '1080.bt1', '1080.dj1', '1080.do1', '1080.fe1', '1080.fn1', '1620.bi1', '1620.bk1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [183845, 456053207518, 87262035388, 83606375, 143975, 80787], 'label': '77760.bo.540.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.by1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.by1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057597
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.x1', '270.ba1', '270.bd1', '270.bj1'], 'contains': ['1080.bo1', '1080.bo2', '1080.bp2', '1080.bq1', '1080.bv1', '1080.dh2', '1080.dh3', '1080.di1', '1080.dm1', '1080.fd1', '1080.fm2', '1620.bj1', '1620.bl1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [183845, 461841090505, 19679028004, 143975, 462320328958, 80787], 'label': '77760.bo.540.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.bz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bz1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057598
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.e1', '12.g1', '18.i1'], 'contains': ['72.b1', '72.e1', '72.g1', '108.i1', '108.j1', '180.bu1', '216.i1', '360.br1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [143975, 286483093054, 85805, 80787, 25470766654, 143304], 'label': '77760.bo.36.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '36.i1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1', 'subgroup_fusion': None, 'weyl_group': '4320.bp'}
  • id: 246057599
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.bz2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.x2', '270.bb1', '270.bc1', '270.bj1'], 'contains': ['1080.bo1', '1080.bo2', '1080.bp1', '1080.bq2', '1080.bv1', '1080.dh1', '1080.dh4', '1080.di2', '1080.dm2', '1080.fd2', '1080.fm1', '1620.bj2', '1620.bl2'], 'core': '4320.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [462320225425, 19678982548, 461841188401, 85805, 80880, 80787], 'label': '77760.bo.540.bz2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.bz2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bz2', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057600
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.y1', '180.bd1', '270.bb1', '270.be1', '270.bh1'], 'contains': ['1080.bp1', '1080.br1', '1080.bw1', '1080.dr1', '1080.ea1', '1080.fg1', '1080.gq1', '1620.bm1', '1620.bn1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [183845, 87182277597, 482849425, 143975, 375138172555, 80787], 'label': '77760.bo.540.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '540.ca1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ca1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057601
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.g1', '180.z1', '270.bc1', '270.be1', '270.bi1'], 'contains': ['1080.bp1', '1080.bs1', '1080.dl1', '1080.ec1', '1080.fo1', '1620.bo1', '1620.bp1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [87261834480, 83543044, 456053073961, 85805, 80880, 80787], 'label': '77760.bo.540.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '540.cb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.cb1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057602
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.ba1', '180.bb1', '180.bc1', '270.bd1', '270.be1', '270.bj1'], 'contains': ['1080.bp1', '1080.bp2', '1080.bw1', '1080.dk1', '1080.dk2', '1080.ee1', '1080.gv1', '1620.bq1', '1620.br1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [461841223825, 183845, 19679028004, 143975, 462320328958, 80787], 'label': '77760.bo.540.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1', 'old_label': '540.cc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.cc1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 246057603
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.be1', '270.bb1', '270.bg1'], 'contains': ['1080.bq2', '1080.br1', '1080.bt1', '1080.ey1', '1080.fa1', '1080.ft1', '1080.fv1', '1620.bs1', '1620.bw1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [7185029309, 19678982548, 462320328958, 85805, 80880, 80787], 'label': '77760.bo.540.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.cd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.cd1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057604
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.bf1', '270.bc1', '270.bf1', '270.bg1'], 'contains': ['1080.bq2', '1080.bs1', '1080.bu1', '1080.ez1', '1080.fb1', '1080.fu1', '1080.fw1', '1620.bt1', '1620.bx1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [462320225425, 7185162389, 19678982548, 85805, 80880, 80787], 'label': '77760.bo.540.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.ce1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ce1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057605
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.bg1', '270.ba1', '270.bb1', '270.bh1'], 'contains': ['1080.bq1', '1080.br1', '1080.bv1', '1080.ev1', '1080.ex1', '1080.fp1', '1080.fr1', '1620.bu1', '1620.by1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87181925066, 482635916, 85805, 375138172555, 80880, 80787], 'label': '77760.bo.540.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.cf1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.cf1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057606
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.k1', '180.bh1', '270.ba1', '270.bf1', '270.bi1'], 'contains': ['1080.bq1', '1080.bs1', '1080.eu1', '1080.fc1', '1080.fz1', '1620.bv1', '1620.bz1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [183845, 456053207518, 83543730, 87262035388, 143975, 80787], 'label': '77760.bo.540.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.cg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.cg1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057607
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.bi1', '270.ba1', '270.bc1', '270.bk1'], 'contains': ['1080.bs1', '1080.bv1', '1080.gb1', '1080.gc1', '1080.gg1', '1620.ca1', '1620.cb1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [355938463434, 87182277597, 374659170505, 85805, 80880, 80787], 'label': '77760.bo.540.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.ch1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ch1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057608
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.bk1', '180.bl1', '180.bm1', '270.bd1', '270.bf1', '270.bh1'], 'contains': ['1080.bq1', '1080.bu1', '1080.bw1', '1080.ew1', '1080.fq1', '1080.gj1', '1080.gx1', '1620.cc1', '1620.ce1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87181925066, 482635561, 85805, 375138172555, 80880, 80787], 'label': '77760.bo.540.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.ci1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ci1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057609
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1'], 'contains': ['72.c1', '72.d1', '72.f1', '72.i1', '72.j1', '108.k1', '180.bw1'], 'core': '720.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [143975, 80787, 143304, 269202533759, 85805, 181146153355, 80880, 267842050314], 'label': '77760.bo.36.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '36.j1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1', 'subgroup_fusion': None, 'weyl_group': '2160.cr'}
  • id: 246057610
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.bj1', '180.bn1', '270.bb1', '270.bf1', '270.bj1'], 'contains': ['1080.bq1', '1080.bq2', '1080.bw1', '1080.et1', '1080.et2', '1080.gm1', '1080.hc1', '1620.cd1', '1620.cf1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [183845, 448908283441, 19679028004, 143975, 80787, 462320328241], 'label': '77760.bo.540.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '540.cj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.cj1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057611
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.bo1', '180.bp1', '180.bq1', '270.bb1', '270.bd1', '270.bk1'], 'contains': ['1080.bt1', '1080.bv1', '1080.bw1', '1080.gd1', '1080.ge1', '1080.hk1', '1080.hs1', '1620.cg1', '1620.ch1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [374659170505, 87181925066, 355938243989, 85805, 80880, 80787], 'label': '77760.bo.540.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.ck1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ck1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057612
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.br1', '180.bs1', '270.be1', '270.bf1', '270.bk1'], 'contains': ['1080.bs1', '1080.bw1', '1080.gf1', '1080.hn1', '1080.hz1', '1620.ci1', '1620.cj1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [374659170505, 87181925066, 355938110909, 85805, 80880, 80787], 'label': '77760.bo.540.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '540.cl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.cl1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057613
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.bt1', '180.bv1', '270.bh1', '270.bi1', '270.bj1'], 'contains': ['1080.o1', '1080.r1', '1080.w1', '1080.bo1', '1080.bp1', '1080.bq1', '1080.bx1', '1080.by1', '1080.ck1', '1080.cn1', '1080.cs1', '1620.ck1', '1620.co1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [442641386187, 443120250115, 143975, 85805, 80787, 143304], 'label': '77760.bo.540.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.cm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.cm1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057614
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.cm2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4860.by1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.bv2', '270.bg1', '270.bj1'], 'contains': ['1080.o2', '1080.r2', '1080.w2', '1080.bo2', '1080.bp2', '1080.bq2', '1080.bx1', '1080.by1', '1080.ck2', '1080.cn2', '1080.cs2', '1620.ck2', '1620.co2'], 'core': '4320.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [442641386187, 143975, 448908284158, 85805, 80787, 143304], 'label': '77760.bo.540.cm2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.cm2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.cm2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246057615
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.k1', '180.bw1', '270.bg1', '270.bh1'], 'contains': ['1080.x1', '1080.ba1', '1080.br1', '1080.bu1', '1080.by1', '1080.cu1', '1080.cx1', '1620.cl1', '1620.cp1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [267845679358, 443120250115, 143975, 85805, 80787, 143304], 'label': '77760.bo.540.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.cn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.cn1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057616
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.n1', '180.bx1', '270.bg1', '270.bi1', '270.bk1'], 'contains': ['1080.y1', '1080.z1', '1080.bs1', '1080.bt1', '1080.by1', '1080.cv1', '1080.cw1', '1620.cm1', '1620.cq1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [482849425, 143975, 85805, 80787, 88695348625, 143304], 'label': '77760.bo.540.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.co1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.co1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057617
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.bu1', '180.by1', '270.bh1', '270.bj1', '270.bk1'], 'contains': ['1080.bb1', '1080.be1', '1080.bv1', '1080.bw1', '1080.by1', '1080.ct1', '1080.db1', '1620.cn1', '1620.cr1'], 'core': '4320.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [268244570163, 85805, 80880, 80787, 274467916948, 143304], 'label': '77760.bo.540.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '540.cp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.cp1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057618
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.cc1', '180.cd1', '270.x1', '270.bl1', '270.bn1'], 'contains': ['1080.cg1', '1080.eg1', '1080.gw1', '1620.cz1', '1620.da1', '1620.db1', '2160.bo1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [178680, 355462911480, 462320052004, 87661145547, 80787, 375138086400], 'label': '77760.bo.540.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '540.cq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.cq1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246057619
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.l1', '180.ce1', '180.cf1', '270.y1', '270.bm1', '270.bn1'], 'contains': ['1080.cg1', '1080.en1', '1080.gz1', '1620.cx1', '1620.dc1', '2160.bp1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [443120071204, 180667209003, 224184, 442641024000, 442162022400, 80787], 'label': '77760.bo.540.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '540.cr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.cr1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246057620
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1', '12.i1', '18.h1', '18.j1', '18.k1'], 'contains': ['72.a1', '108.n1', '216.j1', '360.bx1', '540.cy1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [362615, 274511462400, 87182202116, 80787], 'label': '77760.bo.36.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.k1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1', 'subgroup_fusion': None, 'weyl_group': '1440.5842'}
  • id: 246057621
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.bz1', '180.cg1', '270.e1'], 'contains': ['1080.ce1', '1080.ch1', '1080.cj1', '1080.eq1', '1080.ib1', '4860.w1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [83462998, 598, 456053154955, 174400128000, 180587232000, 93448857600], 'label': '77760.bo.540.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.e1', 'old_label': '540.cs1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.cs1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246057622
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.f1', '180.ca1', '180.ch1', '180.ci1', '270.e1'], 'contains': ['1080.ce1', '1080.ci1', '1080.er1', '1080.es1', '1080.ie1', '4860.bb1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [456053069398, 83462998, 598, 174400128000, 180587232000, 93448857600], 'label': '77760.bo.540.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1', 'old_label': '540.ct1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ct1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246057623
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.cj1', '270.x1', '270.bm1', '270.bo1'], 'contains': ['1080.cg1', '1080.gn1', '1620.di1', '1620.dm1', '2160.bu1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [19679028004, 461841050404, 80787, 262496586694, 462320046985, 693], 'label': '77760.bo.540.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '540.cu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.cu1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057624
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.m1', '180.ck1', '270.y1', '270.bl1', '270.bo1'], 'contains': ['1080.cg1', '1080.gr1', '1620.dj1', '1620.dk1', '1620.dl1', '2160.bx1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [443120071204, 180667289547, 178680, 442162022400, 442641109705, 80787], 'label': '77760.bo.540.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '540.cv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.cv1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057625
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.cl1', '270.z1', '270.bl1', '270.bm1'], 'contains': ['1080.cg1', '1080.ho1', '1620.dn1', '1620.do1', '1620.dp1', '2160.by1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [87182277597, 362615, 355938105600, 262972241015, 80787, 374659447415], 'label': '77760.bo.540.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '540.cw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.cw1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057626
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.g1', '180.cb1', '180.cm1', '270.e1'], 'contains': ['1080.ch1', '1080.ci1', '1080.ic1', '1080.id1', '4860.bg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [83548555, 456053154955, 174400128000, 180587232000, 93448857600, 693], 'label': '77760.bo.540.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.e1', 'old_label': '540.cx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.cx1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 246057627
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.k1', '180.cn1', '180.co1', '270.z1', '270.bn1', '270.bo1'], 'contains': ['1080.cg1', '1080.hu1', '1080.if1', '1620.dq1', '1620.dr1', '2160.bs1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [362615, 355938105600, 87182202116, 262972241015, 80787, 374659447415], 'label': '77760.bo.540.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.b1', 'old_label': '540.cy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.cy1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 246057628
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.cp1', '270.bj1', '270.bp1', '270.bs1'], 'contains': ['1080.ck1', '1080.ck2', '1080.cn2', '1080.cs1', '1080.ct1', '1080.dh3', '1080.dh4', '1080.di1', '1080.dk1', '1080.et2', '1080.fd2', '1620.cs1', '1620.ds1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841090505, 178680, 462320323320, 19679028004, 143975, 80787], 'label': '77760.bo.540.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.cz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.cz1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057629
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.cz2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.cp2', '270.bj1', '270.bq1', '270.br1'], 'contains': ['1080.ck1', '1080.ck2', '1080.cn1', '1080.cs2', '1080.ct1', '1080.dh1', '1080.dh2', '1080.di2', '1080.dk2', '1080.et1', '1080.fd1', '1620.cs2', '1620.ds2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841090505, 178680, 19679028004, 143975, 462320328485, 80787], 'label': '77760.bo.540.cz2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.cz2', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.cz2', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057630
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['60.q1', '180.cq1', '270.bi1', '270.bq1', '270.bs1'], 'contains': ['1080.cn1', '1080.cs1', '1080.cw1', '1080.dj1', '1080.dl1', '1080.eu1', '1080.fe1', '1620.ct1', '1620.dt1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87261834480, 456053074316, 83543730, 80880, 80787, 693], 'label': '77760.bo.540.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.da1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.da1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057631
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.g1', '12.j1', '18.i1'], 'contains': ['72.g1', '72.k1', '72.o1', '108.l1', '108.o1', '180.ce1', '216.k1', '360.cd1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [174879492452, 362615, 462320052004, 80880, 80787], 'label': '77760.bo.36.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '36.l1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1', 'subgroup_fusion': None, 'weyl_group': '1440.5849'}
  • id: 246057632
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.cr1', '270.bh1', '270.br1', '270.bs1'], 'contains': ['1080.cn1', '1080.ct1', '1080.cx1', '1080.dq1', '1080.dr1', '1080.fp1', '1080.fq1', '1620.cu1', '1620.du1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [443120071204, 442641024148, 180667249346, 80880, 80787, 143304], 'label': '77760.bo.540.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.db1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.db1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057633
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.cs1', '270.bg1', '270.bp1', '270.bw1'], 'contains': ['1080.cn2', '1080.cu1', '1080.cv1', '1080.du1', '1080.dv1', '1080.ft1', '1080.fu1', '1620.cv1', '1620.dv1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [178680, 462320323320, 19679028004, 143975, 80787, 7185202680], 'label': '77760.bo.540.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.dc1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.dc1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246057634
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.ct1', '270.bg1', '270.bs1'], 'contains': ['1080.cn2', '1080.cw1', '1080.cx1', '1080.dw1', '1080.dx1', '1080.fv1', '1080.fw1', '1620.cw1', '1620.dw1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [7185207845, 462320323320, 19679028004, 143975, 80787, 143304], 'label': '77760.bo.540.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.dd1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.dd1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057635
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.cs1', '270.bx1'], 'contains': ['1080.co2', '1080.cy1', '1080.cz1', '1080.dy1', '1080.dz1', '1080.fx1', '1080.fy1', '1620.cv1', '1620.dx1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [178680, 462320323467, 19679028004, 80787, 7185202680, 179159], 'label': '77760.bo.540.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '540.de1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.de1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 246057636
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.ce1', '180.cu1', '270.bh1', '270.bq1', '270.bw1'], 'contains': ['1080.cn1', '1080.cu1', '1080.db1', '1080.ds1', '1080.ea1', '1080.fr1', '1080.gx1', '1620.cx1', '1620.dy1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [443120071204, 180667209003, 442641024148, 80880, 80787, 143304], 'label': '77760.bo.540.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.df1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.df1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246057637
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.cf1', '180.cu1', '270.bx1'], 'contains': ['1080.co1', '1080.cy1', '1080.dc1', '1080.dt1', '1080.eb1', '1080.fs1', '1080.gy1', '1620.cx1', '1620.dz1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [443120204759, 180667209003, 224184, 442641386284, 80787, 179159], 'label': '77760.bo.540.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '540.dg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.dg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246057638
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.r1', '180.cv1', '270.bi1', '270.br1', '270.bw1'], 'contains': ['1080.cn1', '1080.cv1', '1080.do1', '1080.ec1', '1080.fz1', '1620.cy1', '1620.ea1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [224184, 83543730, 87262035388, 143975, 456053150130, 80787], 'label': '77760.bo.540.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.dh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.dh1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246057639
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.s1', '180.cv1', '270.bx1'], 'contains': ['1080.co1', '1080.cz1', '1080.dp1', '1080.ed1', '1080.ga1', '1620.cy1', '1620.eb1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [178680, 83543730, 87262035144, 456053150130, 80787, 179159], 'label': '77760.bo.540.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '540.di1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.di1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246057640
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.cc1', '180.cw1', '270.bj1', '270.bs1', '270.bw1'], 'contains': ['1080.cn1', '1080.cn2', '1080.db1', '1080.dm1', '1080.dm2', '1080.ee1', '1080.hc1', '1620.cz1', '1620.ec1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [448908278999, 224184, 462320323320, 19679028004, 143975, 80787], 'label': '77760.bo.540.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '540.dj1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.dj1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057641
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.eb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.cd1', '180.cw1', '270.bx1'], 'contains': ['1080.co1', '1080.co2', '1080.dc1', '1080.dn1', '1080.dn2', '1080.ef1', '1080.hd1', '1620.cz1', '1620.ed1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [448908278999, 462320323467, 19679028004, 80787, 143304, 179159], 'label': '77760.bo.540.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '540.dk1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.dk1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 246057642
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.h1', '12.j1'], 'contains': ['72.h1', '72.l1', '72.p1', '108.l1', '108.p1', '180.cf1', '216.m1', '360.ce1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [479363884, 178680, 443555763716, 80787, 179159], 'label': '77760.bo.36.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.m1', 'old_label': '36.m1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 246057643
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.cc1', '270.u1', '270.bt1', '270.by1'], 'contains': ['1080.dd1', '1080.ej1', '1080.he1', '1620.da1', '1620.ec1', '2160.cd1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841004800, 462320368587, 262496506293, 19678982400, 143975, 143304], 'label': '77760.bo.540.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '540.dl1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.dl1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057644
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.cc1', '270.bu1'], 'contains': ['1080.de1', '1080.ek1', '1080.hf1', '1620.db1', '1620.ec1', '2160.ce1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [461841004948, 19678982548, 462320006400, 148, 262496586694, 693], 'label': '77760.bo.540.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.z1', 'old_label': '540.dm1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.dm1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057645
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.cd1', '270.bz1'], 'contains': ['1080.df1', '1080.el1', '1080.hg1', '1620.da1', '1620.ed1', '2160.cf1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [462320368684, 375138265559, 178680, 355462911480, 87661100280, 179159], 'label': '77760.bo.540.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '540.dn1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.dn1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057646
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.cd1'], 'contains': ['1080.dg1', '1080.em1', '1080.hh1', '1620.db1', '1620.ed1', '2160.cg1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 360, 'diagramx': None, 'generators': [462320368684, 375138265559, 178680, 87661100280, 355462956747, 179159], 'label': '77760.bo.540.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.cd1', 'old_label': '540.do1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.do1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 246057647
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.o1', '180.ce1', '270.v1', '270.bv1', '270.by1'], 'contains': ['1080.dd1', '1080.eo1', '1080.hi1', '1620.dc1', '1620.dy1', '2160.ch1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [482854584, 188331269880, 87182063304, 80880, 375138086400, 143304], 'label': '77760.bo.540.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '540.dp1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.dp1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057648
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.p1', '180.cf1', '270.bz1'], 'contains': ['1080.df1', '1080.ep1', '1080.hj1', '1620.dc1', '1620.dz1', '2160.ci1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [375138265559, 188331269880, 482809080, 178680, 87182282615, 179159], 'label': '77760.bo.540.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '540.dq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.dq1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057649
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.cx1', '270.bh1', '270.bp1', '270.bq1'], 'contains': ['1080.cs1', '1080.ct1', '1080.cu1', '1080.ev1', '1080.ew1', '1080.ff1', '1080.fg1', '1620.dd1', '1620.ee1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [178680, 143975, 80787, 180667203842, 443120250115, 442641300482], 'label': '77760.bo.540.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.dr1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.dr1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057650
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.cy1', '270.bg1', '270.bq1'], 'contains': ['1080.cs2', '1080.cu1', '1080.cw1', '1080.ey1', '1080.fb1', '1080.fi1', '1080.fl1', '1620.de1', '1620.ef1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [178680, 19679028004, 143975, 462320328485, 80787, 7185202680], 'label': '77760.bo.540.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.ds1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ds1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057651
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.cz1', '270.bg1', '270.br1', '270.ca1'], 'contains': ['1080.cs2', '1080.cv1', '1080.cx1', '1080.ez1', '1080.fa1', '1080.fj1', '1080.fk1', '1620.df1', '1620.eg1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [7185207845, 19679028004, 143975, 80787, 462320328386, 143304], 'label': '77760.bo.540.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.dt1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.dt1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 246057652
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.t1', '180.da1', '270.bi1', '270.bp1', '270.ca1'], 'contains': ['1080.cs1', '1080.cv1', '1080.fc1', '1080.fn1', '1080.fo1', '1620.dg1', '1620.eh1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [83548555, 87262035388, 456053154955, 143975, 80787, 143304], 'label': '77760.bo.540.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.du1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.du1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057653
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '77760.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.i1', '12.k1', '18.i1'], 'contains': ['72.g1', '72.m1', '72.n1', '108.m1', '108.q1', '180.ck1', '216.l1', '360.ch1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [362615, 443555839197, 479087546, 80880, 80787], 'label': '77760.bo.36.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '36.n1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1', 'subgroup_fusion': None, 'weyl_group': '4320.bp'}
  • id: 246057654
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.db1', '270.bk1', '270.bp1', '270.br1'], 'contains': ['1080.ct1', '1080.cv1', '1080.gc1', '1080.ge1', '1080.gf1', '1620.dh1', '1620.ei1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [87182277597, 178680, 374659447555, 143975, 355938110909, 80787], 'label': '77760.bo.540.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.dv1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.dv1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057655
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.cj1', '270.u1', '270.bv1', '270.cb1'], 'contains': ['1080.dd1', '1080.gi1', '1080.gp1', '1620.di1', '1620.ek1', '2160.cn1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841004800, 262496506293, 19678982400, 143975, 462320328386, 143304], 'label': '77760.bo.540.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.dw1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.dw1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057656
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.ck1', '180.dc1', '270.bh1', '270.bs1', '270.ca1'], 'contains': ['1080.cs1', '1080.cx1', '1080.db1', '1080.ex1', '1080.fh1', '1080.gj1', '1080.gq1', '1620.dj1', '1620.ej1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [180667289547, 178680, 442641300482, 443120250115, 143975, 80787], 'label': '77760.bo.540.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.dx1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.dx1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057657
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.q1', '180.ck1', '270.v1', '270.bt1', '270.cb1'], 'contains': ['1080.dd1', '1080.gk1', '1080.gt1', '1620.dk1', '1620.ej1', '2160.cp1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [179012, 178680, 443120204612, 442641300482, 442162022400, 180667244280], 'label': '77760.bo.540.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.dy1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.dy1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057658
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.ck1', '270.bu1'], 'contains': ['1080.de1', '1080.gl1', '1080.gu1', '1620.dl1', '1620.ej1', '2160.cq1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [188331315147, 482854584, 375138172205, 87182063304, 80880, 143304], 'label': '77760.bo.540.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bu1', 'old_label': '540.dz1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.dz1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057659
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9720.bg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.cj1', '180.dd1', '270.bj1', '270.bq1', '270.ca1'], 'contains': ['1080.cs1', '1080.cs2', '1080.db1', '1080.fm1', '1080.fm2', '1080.gm1', '1080.gv1', '1620.dm1', '1620.ek1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [461841004948, 19678982548, 80880, 80787, 462320046985, 143304], 'label': '77760.bo.540.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '540.ea1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ea1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 246057660
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.cl1', '180.de1', '270.bk1', '270.bq1', '270.bs1'], 'contains': ['1080.ct1', '1080.cw1', '1080.db1', '1080.gb1', '1080.gd1', '1080.hk1', '1080.hn1', '1620.dn1', '1620.el1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87182277597, 355938105600, 178680, 374659447555, 143975, 80787], 'label': '77760.bo.540.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.eb1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.eb1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057661
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.cl1', '270.w1', '270.bt1', '270.bv1'], 'contains': ['1080.dd1', '1080.hl1', '1080.hq1', '1620.do1', '1620.el1', '2160.cs1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [87182277597, 355938105600, 143975, 262972241015, 374659447415, 143304], 'label': '77760.bo.540.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1', 'old_label': '540.ec1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ec1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057662
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38880.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.cl1', '270.bu1'], 'contains': ['1080.de1', '1080.hm1', '1080.hr1', '1620.dp1', '1620.el1', '2160.ct1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': None, 'generators': [87182277597, 355938105600, 262972160516, 143975, 374659447415, 143304], 'label': '77760.bo.540.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bu1', 'old_label': '540.ed1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ed1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057663
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.cn1', '180.df1', '270.bk1', '270.bw1', '270.ca1'], 'contains': ['1080.cv1', '1080.db1', '1080.gg1', '1080.hs1', '1080.hz1', '1620.dq1', '1620.em1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [355938105600, 87182202116, 143975, 80787, 374659447415, 143304], 'label': '77760.bo.540.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.ee1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ee1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246057664
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.h1', '18.g1', '18.l1', '18.n1'], 'contains': ['72.q1', '108.n1', '216.n1', '360.cl1', '540.eg1'], 'core': '216.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [274511462400, 143975, 87182282615, 143304], 'label': '77760.bo.36.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.o1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
  • id: 246057665
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.co1', '180.df1', '270.bx1'], 'contains': ['1080.cz1', '1080.dc1', '1080.gh1', '1080.ht1', '1080.ia1', '1620.dq1', '1620.en1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [355938105600, 178680, 87182202116, 80787, 374659447415, 179159], 'label': '77760.bo.540.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '540.ef1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ef1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246057666
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.o1', '180.cn1', '270.w1', '270.by1', '270.cb1'], 'contains': ['1080.dd1', '1080.hx1', '1080.ig1', '1620.dr1', '1620.em1', '2160.cl1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [355938105600, 143975, 262972241015, 87182282615, 374659447415, 143304], 'label': '77760.bo.540.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '540.eg1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.eg1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057667
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.p1', '180.co1', '270.bz1'], 'contains': ['1080.df1', '1080.hy1', '1080.ih1', '1620.dr1', '1620.en1', '2160.cm1'], 'core': '77760.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [355938105600, 178680, 262972241015, 87182282615, 374659447415, 179159], 'label': '77760.bo.540.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.bc1', 'old_label': '540.eh1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.eh1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 246057668
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.dg1', '270.j1', '270.ba1', '270.bs1'], 'contains': ['1080.di1', '1080.dm1', '1080.dx1', '1080.eu1', '1080.ex1', '1080.fp1', '1080.gb1', '1620.eo1', '1620.es1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [448908278999, 461841009961, 462320323320, 19679028004, 143975, 80787], 'label': '77760.bo.540.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.ei1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ei1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057669
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.dg2', '270.h1', '270.bb1', '270.bs1'], 'contains': ['1080.dj1', '1080.dm2', '1080.dr1', '1080.et2', '1080.ex1', '1080.fv1', '1080.gd1', '1620.ep1', '1620.es2'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [462320323799, 448908283441, 19679028004, 143975, 461841183388, 80787], 'label': '77760.bo.540.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.ej1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ej1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057670
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.dh1', '270.j1', '270.bb1', '270.br1'], 'contains': ['1080.di2', '1080.do1', '1080.dr1', '1080.et1', '1080.fa1', '1080.fp1', '1080.ge1', '1620.eq1', '1620.et1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841090505, 448908007104, 19678982548, 462320328958, 80880, 80787], 'label': '77760.bo.540.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.ek1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ek1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057671
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.ce2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.dj1', '270.o1', '270.ba1', '270.bp1'], 'contains': ['1080.di1', '1080.du1', '1080.ev1', '1080.fc1', '1080.gc1', '1620.er1', '1620.fb1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [461841009961, 448908283441, 462320323320, 19679028004, 143975, 80787], 'label': '77760.bo.540.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.el1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.el1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246057672
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.dg2', '270.g1', '270.bc1', '270.bs1'], 'contains': ['1080.dl1', '1080.dm2', '1080.dq1', '1080.fd2', '1080.fh1', '1080.fw1', '1080.gb1', '1620.es2', '1620.eu1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [462320323652, 19679028004, 143975, 461841148348, 448908284158, 80787], 'label': '77760.bo.540.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.em1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.em1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057673
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.dg1', '270.f1', '270.bd1', '270.bs1'], 'contains': ['1080.dk1', '1080.dm1', '1080.dw1', '1080.fe1', '1080.fh1', '1080.fq1', '1080.gd1', '1620.es1', '1620.ev1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [448908278999, 461841090505, 462320052004, 19678982548, 80880, 80787], 'label': '77760.bo.540.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.en1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.en1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057674
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.dh1', '270.g1', '270.bd1', '270.br1'], 'contains': ['1080.dk2', '1080.do1', '1080.dq1', '1080.fd1', '1080.fk1', '1080.fq1', '1080.ge1', '1620.et1', '1620.ew1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841090505, 19679028004, 143975, 462320328958, 80787, 448908278520], 'label': '77760.bo.540.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.eo1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.eo1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057675
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1', '18.m1'], 'contains': ['72.r1', '108.n1', '216.o1', '360.cn1', '540.eh1'], 'core': '216.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [274511462400, 178680, 87182282615, 179159], 'label': '77760.bo.36.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '36.p1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
  • id: 246057676
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.di1', '270.j1', '270.bc1', '270.bq1'], 'contains': ['1080.di2', '1080.dl1', '1080.ds1', '1080.fb1', '1080.ff1', '1080.fm1', '1080.gb1', '1620.ex1', '1620.fa1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [462320225425, 448908001949, 19678982548, 461841188401, 80880, 80787], 'label': '77760.bo.540.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.ep1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ep1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057677
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.di1', '270.h1', '270.bd1', '270.bq1'], 'contains': ['1080.dj1', '1080.dk2', '1080.ds1', '1080.ew1', '1080.fl1', '1080.fm2', '1080.gd1', '1620.ey1', '1620.fa1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841223825, 448908283441, 19679028004, 143975, 462320328958, 80787], 'label': '77760.bo.540.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.eq1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.eq1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057678
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.dk1', '270.j1', '270.bd1', '270.bp1'], 'contains': ['1080.di1', '1080.dk1', '1080.dv1', '1080.ew1', '1080.ff1', '1080.fn1', '1080.ge1', '1620.ez1', '1620.fc1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [461841090505, 462320052004, 19678982548, 80880, 80787, 448908283914], 'label': '77760.bo.540.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.er1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.er1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 246057679
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.dj1', '270.f1', '270.be1', '270.bp1'], 'contains': ['1080.dk1', '1080.du1', '1080.fg1', '1080.fo1', '1080.gf1', '1620.fb1', '1620.fd1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [461841090505, 462320052004, 448908001949, 19678982548, 80880, 80787], 'label': '77760.bo.540.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '540.es1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.es1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057680
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.dl1', '270.f1', '270.ba1', '270.bw1'], 'contains': ['1080.dm1', '1080.du1', '1080.fr1', '1080.fz1', '1080.gg1', '1620.fe1', '1620.ff1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [448908278999, 461841367555, 462320052004, 19678982548, 80880, 80787], 'label': '77760.bo.540.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.et1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.et1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246057681
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.dl1', '270.bx1'], 'contains': ['1080.dn1', '1080.dy1', '1080.fs1', '1080.ga1', '1080.gh1', '1620.fe1', '1620.fg1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [448908278999, 462320323467, 19679028004, 461841228844, 80787, 179159], 'label': '77760.bo.540.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '540.eu1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.eu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 246057682
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.ce2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.dm1', '180.dz1', '270.o1', '270.bb1', '270.bq1'], 'contains': ['1080.di2', '1080.dj1', '1080.ea1', '1080.ev1', '1080.ey1', '1080.gm1', '1080.hk1', '1620.fh1', '1620.fi1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [19678982548, 461841281758, 462320328958, 80880, 80787, 448908283914], 'label': '77760.bo.540.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.ev1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ev1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246057683
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19440.l2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.dm1', '180.ea1', '270.g1', '270.be1', '270.bq1'], 'contains': ['1080.dk2', '1080.dl1', '1080.ea1', '1080.fg1', '1080.fi1', '1080.gv1', '1080.hn1', '1620.fi1', '1620.fj1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [19679028004, 143975, 461841050404, 462320328958, 80787, 448908278520], 'label': '77760.bo.540.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.b1', 'old_label': '540.ew1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ew1', 'subgroup_fusion': None, 'weyl_group': '432.545'}
  • id: 246057684
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['180.dn1', '180.eb1', '270.g1', '270.bb1', '270.bw1'], 'contains': ['1080.dm2', '1080.do1', '1080.ea1', '1080.fr1', '1080.ft1', '1080.hc1', '1080.hs1', '1620.fk1', '1620.fl1'], 'core': '8640.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [462320323799, 143975, 80787, 461841183388, 19679028004, 448908278999], 'label': '77760.bo.540.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.c1', 'old_label': '540.ex1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ex1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 246057685
    {'ambient': '77760.bo', 'aut_centralizer_order': None, 'aut_label': '540.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['180.dn1', '180.ec1', '270.bx1'], 'contains': ['1080.dn2', '1080.dp1', '1080.eb1', '1080.fs1', '1080.fx1', '1080.hd1', '1080.ht1', '1620.fk1', '1620.fm1'], 'core': '25920.a1', 'coset_action_label': None, 'count': 540, 'diagramx': None, 'generators': [462320323891, 19679028004, 461841050404, 448908278667, 80787, 179159], 'label': '77760.bo.540.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.bx1', 'old_label': '540.ey1', 'projective_image': '77760.bo', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ey1', 'subgroup_fusion': None, 'weyl_group': '24.14'}