Abstract group data - 600.157

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• gps_groups •

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

  
  {'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.9', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 40, 'aut_gen_orders': [4, 5, 8, 4, 2, 10, 5, 2], 'aut_gens': [[1, 4, 40], [265, 148, 280], [145, 364, 40], [369, 246, 432], [481, 502, 408], [1, 4, 440], [481, 276, 40], [137, 364, 40], [153, 396, 160]], 'aut_group': '1600.10254', 'aut_hash': 10254, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1600, 'aut_permdeg': 37, 'aut_perms': [3238262482707351533797839011838221359110145, 11600654198913531160649487977849218582916290, 4241628021758069895306228955652874937150401, 8240951998411539081021698694448651078819331, 9333755695734919995571200, 8500901416650935786869085294790108092499064, 9963292272173982211537425289246229004115497, 13352570873795207331426896862794804661925234], 'aut_phi_ratio': 10.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 5, 2, 1], [2, 25, 1, 1], [3, 1, 2, 1], [4, 25, 1, 2], [4, 25, 2, 1], [5, 4, 2, 1], [5, 8, 2, 1], [6, 5, 4, 1], [6, 25, 2, 1], [10, 20, 2, 1], [12, 25, 2, 2], [12, 25, 4, 1], [15, 4, 4, 1], [15, 8, 4, 1], [30, 20, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'F_5^2:C_2^2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 40, 'autcentquo_group': '800.1191', 'autcentquo_hash': 1191, 'autcentquo_nilpotent': False, 'autcentquo_order': 800, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_5\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 5, 2], [2, 25, 1], [3, 1, 2], [4, 25, 4], [5, 4, 2], [5, 8, 2], [6, 5, 4], [6, 25, 2], [10, 20, 2], [12, 25, 8], [15, 4, 4], [15, 8, 4], [30, 20, 4]], 'center_label': '3.1', 'center_order': 3, 'central_product': True, 'central_quotient': '200.42', 'commutator_count': 1, 'commutator_label': '25.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '5.1', '5.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 157, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['200.42', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 5, 1, 2], [2, 25, 1, 1], [3, 1, 2, 1], [4, 25, 2, 2], [5, 4, 1, 2], [5, 8, 1, 2], [6, 5, 2, 2], [6, 25, 2, 1], [10, 20, 1, 2], [12, 25, 4, 2], [15, 4, 2, 2], [15, 8, 2, 2], [30, 20, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 48, 'exponent': 60, 'exponents_of_order': [3, 2, 1], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[8, 0, 4]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '600.157', 'hash': 157, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 20, 'inner_gen_orders': [4, 10, 5], 'inner_gens': [[1, 28, 280], [17, 4, 160], [361, 484, 40]], 'inner_hash': 42, 'inner_nilpotent': False, 'inner_order': 200, 'inner_split': False, 'inner_tex': 'D_5:F_5', 'inner_used': [1, 2, 3], 'irrC_degree': 8, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 16, 'irrep_stats': [[1, 24], [4, 12], [8, 6]], 'label': '600.157', 'linC_count': 36, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 24, 'linQ_dim': 10, 'linQ_dim_count': 24, 'linR_count': 48, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D5^2.C6', 'ngens': 6, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 18, 'number_characteristic_subgroups': 14, 'number_conjugacy_classes': 42, 'number_divisions': 24, 'number_normal_subgroups': 26, 'number_subgroup_autclasses': 50, 'number_subgroup_classes': 76, 'number_subgroups': 504, 'old_label': None, 'order': 600, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 35], [3, 2], [4, 100], [5, 24], [6, 70], [10, 40], [12, 200], [15, 48], [30, 80]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [22, 2, 0], 'outer_gens': [[1, 12, 40], [1, 12, 320], [1, 142, 408]], 'outer_group': '8.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [1, 6, 120], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 13, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 6], [8, 6], [16, 2]], 'representations': {'PC': {'code': 28063286802408873369098244177140948766904375, 'gens': [1, 3, 5], 'pres': [6, -2, -2, -2, -5, -3, -5, 12, 506, 332, 50, 387, 393, 8404, 2410, 1216, 118, 8645, 8651, 4337]}, 'Perm': {'d': 13, 'gens': [43908489, 16, 5760, 87091216, 46, 606009600]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 12], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_5^2.C_6', 'transitive_degree': 30, '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: 139586786
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 157, 'group_order': 600, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 139586797
    {'aut_label': '2A', 'centralizer': '5.a1.a1', 'counter': 2, 'group_counter': 157, 'group_order': 600, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 260, 'size': 5}
  • id: 139586808
    {'aut_label': '2A', 'centralizer': '5.a1.b1', 'counter': 3, 'group_counter': 157, 'group_order': 600, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 6, 'size': 5}
  • id: 139586819
    {'aut_label': '2C', 'centralizer': '25.a1.a1', 'counter': 4, 'group_counter': 157, 'group_order': 600, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 138, 'size': 25}
  • id: 139586823
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 5, 'group_counter': 157, 'group_order': 600, 'label': '3A1', 'order': 3, 'powers': [6, 1, 6], 'representative': 200, 'size': 1}
  • id: 139586824
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 6, 'group_counter': 157, 'group_order': 600, 'label': '3A-1', 'order': 3, 'powers': [5, 1, 5], 'representative': 400, 'size': 1}
  • id: 139586825
    {'aut_label': '4A1', 'centralizer': '25.a1.a1', 'counter': 7, 'group_counter': 157, 'group_order': 600, 'label': '4A1', 'order': 4, 'powers': [4, 8, 7], 'representative': 273, 'size': 25}
  • id: 139586826
    {'aut_label': '4A-1', 'centralizer': '25.a1.a1', 'counter': 8, 'group_counter': 157, 'group_order': 600, 'label': '4A-1', 'order': 4, 'powers': [4, 7, 8], 'representative': 507, 'size': 25}
  • id: 139586827
    {'aut_label': '4B1', 'centralizer': '25.a1.a1', 'counter': 9, 'group_counter': 157, 'group_order': 600, 'label': '4B1', 'order': 4, 'powers': [4, 10, 9], 'representative': 151, 'size': 25}
  • id: 139586787
    {'aut_label': '4B1', 'centralizer': '25.a1.a1', 'counter': 10, 'group_counter': 157, 'group_order': 600, 'label': '4B-1', 'order': 4, 'powers': [4, 9, 10], 'representative': 245, 'size': 25}
  • id: 139586788
    {'aut_label': '5A', 'centralizer': '4.a1.a1', 'counter': 11, 'group_counter': 157, 'group_order': 600, 'label': '5A', 'order': 5, 'powers': [11, 11, 1], 'representative': 24, 'size': 4}
  • id: 139586789
    {'aut_label': '5A', 'centralizer': '4.a1.b1', 'counter': 12, 'group_counter': 157, 'group_order': 600, 'label': '5B', 'order': 5, 'powers': [12, 12, 1], 'representative': 240, 'size': 4}
  • id: 139586790
    {'aut_label': '5C', 'centralizer': '8.a1.a1', 'counter': 13, 'group_counter': 157, 'group_order': 600, 'label': '5C', 'order': 5, 'powers': [13, 13, 1], 'representative': 144, 'size': 8}
  • id: 139586791
    {'aut_label': '5C', 'centralizer': '8.a1.a1', 'counter': 14, 'group_counter': 157, 'group_order': 600, 'label': '5D', 'order': 5, 'powers': [14, 14, 1], 'representative': 264, 'size': 8}
  • id: 139586792
    {'aut_label': '6A1', 'centralizer': '5.a1.a1', 'counter': 15, 'group_counter': 157, 'group_order': 600, 'label': '6A1', 'order': 6, 'powers': [6, 2, 16], 'representative': 460, 'size': 5}
  • id: 139586793
    {'aut_label': '6A1', 'centralizer': '5.a1.a1', 'counter': 16, 'group_counter': 157, 'group_order': 600, 'label': '6A-1', 'order': 6, 'powers': [5, 2, 15], 'representative': 60, 'size': 5}
  • id: 139586794
    {'aut_label': '6A1', 'centralizer': '5.a1.b1', 'counter': 17, 'group_counter': 157, 'group_order': 600, 'label': '6B1', 'order': 6, 'powers': [6, 3, 18], 'representative': 206, 'size': 5}
  • id: 139586795
    {'aut_label': '6A1', 'centralizer': '5.a1.b1', 'counter': 18, 'group_counter': 157, 'group_order': 600, 'label': '6B-1', 'order': 6, 'powers': [5, 3, 17], 'representative': 406, 'size': 5}
  • id: 139586796
    {'aut_label': '6C1', 'centralizer': '25.a1.a1', 'counter': 19, 'group_counter': 157, 'group_order': 600, 'label': '6C1', 'order': 6, 'powers': [6, 4, 20], 'representative': 338, 'size': 25}
  • id: 139586798
    {'aut_label': '6C1', 'centralizer': '25.a1.a1', 'counter': 20, 'group_counter': 157, 'group_order': 600, 'label': '6C-1', 'order': 6, 'powers': [5, 4, 19], 'representative': 538, 'size': 25}
  • id: 139586799
    {'aut_label': '10A', 'centralizer': '20.b1.a1', 'counter': 21, 'group_counter': 157, 'group_order': 600, 'label': '10A', 'order': 10, 'powers': [11, 21, 2], 'representative': 252, 'size': 20}
  • id: 139586800
    {'aut_label': '10A', 'centralizer': '20.b1.b1', 'counter': 22, 'group_counter': 157, 'group_order': 600, 'label': '10B', 'order': 10, 'powers': [12, 22, 3], 'representative': 126, 'size': 20}
  • id: 139586801
    {'aut_label': '12A1', 'centralizer': '25.a1.a1', 'counter': 23, 'group_counter': 157, 'group_order': 600, 'label': '12A1', 'order': 12, 'powers': [19, 7, 25], 'representative': 307, 'size': 25}
  • id: 139586802
    {'aut_label': '12A-1', 'centralizer': '25.a1.a1', 'counter': 24, 'group_counter': 157, 'group_order': 600, 'label': '12A-1', 'order': 12, 'powers': [20, 8, 26], 'representative': 473, 'size': 25}
  • id: 139586803
    {'aut_label': '12A1', 'centralizer': '25.a1.a1', 'counter': 25, 'group_counter': 157, 'group_order': 600, 'label': '12A5', 'order': 12, 'powers': [20, 7, 23], 'representative': 107, 'size': 25}
  • id: 139586804
    {'aut_label': '12A-1', 'centralizer': '25.a1.a1', 'counter': 26, 'group_counter': 157, 'group_order': 600, 'label': '12A-5', 'order': 12, 'powers': [19, 8, 24], 'representative': 73, 'size': 25}
  • id: 139586805
    {'aut_label': '12B1', 'centralizer': '25.a1.a1', 'counter': 27, 'group_counter': 157, 'group_order': 600, 'label': '12B1', 'order': 12, 'powers': [19, 9, 29], 'representative': 45, 'size': 25}
  • id: 139586806
    {'aut_label': '12B1', 'centralizer': '25.a1.a1', 'counter': 28, 'group_counter': 157, 'group_order': 600, 'label': '12B-1', 'order': 12, 'powers': [20, 10, 30], 'representative': 351, 'size': 25}
  • id: 139586807
    {'aut_label': '12B1', 'centralizer': '25.a1.a1', 'counter': 29, 'group_counter': 157, 'group_order': 600, 'label': '12B5', 'order': 12, 'powers': [20, 9, 27], 'representative': 445, 'size': 25}
  • id: 139586809
    {'aut_label': '12B1', 'centralizer': '25.a1.a1', 'counter': 30, 'group_counter': 157, 'group_order': 600, 'label': '12B-5', 'order': 12, 'powers': [19, 10, 28], 'representative': 551, 'size': 25}
  • id: 139586810
    {'aut_label': '15A1', 'centralizer': '4.a1.a1', 'counter': 31, 'group_counter': 157, 'group_order': 600, 'label': '15A1', 'order': 15, 'powers': [32, 11, 6], 'representative': 208, 'size': 4}
  • id: 139586811
    {'aut_label': '15A1', 'centralizer': '4.a1.a1', 'counter': 32, 'group_counter': 157, 'group_order': 600, 'label': '15A-1', 'order': 15, 'powers': [31, 11, 5], 'representative': 432, 'size': 4}
  • id: 139586812
    {'aut_label': '15A1', 'centralizer': '4.a1.b1', 'counter': 33, 'group_counter': 157, 'group_order': 600, 'label': '15B1', 'order': 15, 'powers': [34, 12, 6], 'representative': 80, 'size': 4}
  • id: 139586813
    {'aut_label': '15A1', 'centralizer': '4.a1.b1', 'counter': 34, 'group_counter': 157, 'group_order': 600, 'label': '15B-1', 'order': 15, 'powers': [33, 12, 5], 'representative': 520, 'size': 4}
  • id: 139586814
    {'aut_label': '15C1', 'centralizer': '8.a1.a1', 'counter': 35, 'group_counter': 157, 'group_order': 600, 'label': '15C1', 'order': 15, 'powers': [36, 13, 5], 'representative': 48, 'size': 8}
  • id: 139586815
    {'aut_label': '15C1', 'centralizer': '8.a1.a1', 'counter': 36, 'group_counter': 157, 'group_order': 600, 'label': '15C-1', 'order': 15, 'powers': [35, 13, 6], 'representative': 96, 'size': 8}
  • id: 139586816
    {'aut_label': '15C1', 'centralizer': '8.a1.a1', 'counter': 37, 'group_counter': 157, 'group_order': 600, 'label': '15D1', 'order': 15, 'powers': [38, 14, 6], 'representative': 88, 'size': 8}
  • id: 139586817
    {'aut_label': '15C1', 'centralizer': '8.a1.a1', 'counter': 38, 'group_counter': 157, 'group_order': 600, 'label': '15D-1', 'order': 15, 'powers': [37, 14, 5], 'representative': 56, 'size': 8}
  • id: 139586818
    {'aut_label': '30A1', 'centralizer': '20.b1.a1', 'counter': 39, 'group_counter': 157, 'group_order': 600, 'label': '30A1', 'order': 30, 'powers': [31, 21, 15], 'representative': 44, 'size': 20}
  • id: 139586820
    {'aut_label': '30A1', 'centralizer': '20.b1.a1', 'counter': 40, 'group_counter': 157, 'group_order': 600, 'label': '30A-1', 'order': 30, 'powers': [32, 21, 16], 'representative': 84, 'size': 20}
  • id: 139586821
    {'aut_label': '30A1', 'centralizer': '20.b1.b1', 'counter': 41, 'group_counter': 157, 'group_order': 600, 'label': '30B1', 'order': 30, 'powers': [33, 22, 17], 'representative': 46, 'size': 20}
  • id: 139586822
    {'aut_label': '30A1', 'centralizer': '20.b1.b1', 'counter': 42, 'group_counter': 157, 'group_order': 600, 'label': '30B-1', 'order': 30, 'powers': [34, 22, 18], 'representative': 86, 'size': 20}
• 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: 12743493
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '600.157', 'group_order': 600, 'image': None, 'label': '600.157.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12743504
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '600.157', 'group_order': 600, 'image': None, 'label': '600.157.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12743510
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '600.157', 'group_order': 600, 'image': None, 'label': '600.157.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12743511
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '600.157', 'group_order': 600, 'image': None, 'label': '600.157.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12743512
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '600.157', 'group_order': 600, 'image': None, 'label': '600.157.1e', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12743513
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '600.157', 'group_order': 600, 'image': None, 'label': '600.157.1f', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, 2, 2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2], 'schur_index': 1}
  • id: 12743514
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '600.157', 'group_order': 600, 'image': None, 'label': '600.157.1g', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2], 'schur_index': 1}
  • id: 12743515
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '600.157', 'group_order': 600, 'image': None, 'label': '600.157.1h', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -1, -1, -2, -2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, -1, -1, -2, -2, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12743516
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '600.157', 'group_order': 600, 'image': None, 'label': '600.157.1i', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -1, -1, 2, 2, -2, -2, 2, 2, 2, 2, 1, 1, 1, 1, -1, -1, -2, -2, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12743494
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '600.157', 'group_order': 600, 'image': None, 'label': '600.157.1j', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, -1, -2, -2, -2, -2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12743495
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '600.157', 'group_order': 600, 'image': None, 'label': '600.157.1k', 'multiplicity': 4, 'nt': [12, 1], 'qdim': 4, 'qvalues': [4, -4, 4, -4, -2, -2, 0, 0, 0, 0, 4, 4, 4, 4, 2, 2, -2, -2, 2, 2, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2], 'schur_index': 1}
  • id: 12743496
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '600.157', 'group_order': 600, 'image': None, 'label': '600.157.1l', 'multiplicity': 4, 'nt': [12, 1], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -2, -2, 0, 0, 0, 0, 4, 4, 4, 4, -2, -2, 2, 2, 2, 2, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, -2, -2], 'schur_index': 1}
  • id: 12743497
    {'cdim': 4, 'counter': 13, 'faithful': False, 'group': '600.157', 'group_order': 600, 'image': None, 'label': '600.157.4a', 'multiplicity': 1, 'nt': [5, 3], 'qdim': 4, 'qvalues': [4, 0, 4, 0, 4, 4, 0, 0, 0, 0, 4, -1, -1, -1, 0, 0, 4, 4, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 4, 4, -1, -1, -1, -1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 12743498
    {'cdim': 4, 'counter': 14, 'faithful': False, 'group': '600.157', 'group_order': 600, 'image': None, 'label': '600.157.4b', 'multiplicity': 1, 'nt': [5, 3], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 4, 0, 0, 0, 0, -1, 4, -1, -1, 4, 4, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -1, -1, -1, -1, -1, -1, 0, 0, -1, -1], 'schur_index': 1}
  • id: 12743499
    {'cdim': 4, 'counter': 15, 'faithful': False, 'group': '600.157', 'group_order': 600, 'image': None, 'label': '600.157.4c', 'multiplicity': 1, 'nt': [10, 5], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 4, 4, 0, 0, 0, 0, -1, 4, -1, -1, -4, -4, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -1, -1, -1, -1, -1, -1, 0, 0, 1, 1], 'schur_index': 1}
  • id: 12743500
    {'cdim': 4, 'counter': 16, 'faithful': False, 'group': '600.157', 'group_order': 600, 'image': None, 'label': '600.157.4d', 'multiplicity': 1, 'nt': [10, 5], 'qdim': 4, 'qvalues': [4, 0, -4, 0, 4, 4, 0, 0, 0, 0, 4, -1, -1, -1, 0, 0, -4, -4, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 4, 4, -1, -1, -1, -1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 12743501
    {'cdim': 4, 'counter': 17, 'faithful': False, 'group': '600.157', 'group_order': 600, 'image': None, 'label': '600.157.4e', 'multiplicity': 2, 'nt': [15, 8], 'qdim': 8, 'qvalues': [8, 0, 8, 0, -4, -4, 0, 0, 0, 0, 8, -2, -2, -2, 0, 0, -4, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -4, -4, 1, 1, 1, 1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 12743502
    {'cdim': 4, 'counter': 18, 'faithful': False, 'group': '600.157', 'group_order': 600, 'image': None, 'label': '600.157.4f', 'multiplicity': 2, 'nt': [15, 8], 'qdim': 8, 'qvalues': [8, 8, 0, 0, -4, -4, 0, 0, 0, 0, -2, 8, -2, -2, -4, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1], 'schur_index': 1}
  • id: 12743503
    {'cdim': 4, 'counter': 19, 'faithful': False, 'group': '600.157', 'group_order': 600, 'image': None, 'label': '600.157.4g', 'multiplicity': 2, 'nt': [30, 26], 'qdim': 8, 'qvalues': [8, -8, 0, 0, -4, -4, 0, 0, 0, 0, -2, 8, -2, -2, 4, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 1, 1, 1, 1, 1, 1, 0, 0, -1, -1], 'schur_index': 1}
  • id: 12743505
    {'cdim': 4, 'counter': 20, 'faithful': False, 'group': '600.157', 'group_order': 600, 'image': None, 'label': '600.157.4h', 'multiplicity': 2, 'nt': [30, 26], 'qdim': 8, 'qvalues': [8, 0, -8, 0, -4, -4, 0, 0, 0, 0, 8, -2, -2, -2, 0, 0, 4, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -4, -4, 1, 1, 1, 1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 12743506
    {'cdim': 8, 'counter': 21, 'faithful': False, 'group': '600.157', 'group_order': 600, 'image': None, 'label': '600.157.8a', 'multiplicity': 1, 'nt': [10, 17], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 8, 8, 0, 0, 0, 0, -2, -2, -2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 3, 3, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12743507
    {'cdim': 8, 'counter': 22, 'faithful': False, 'group': '600.157', 'group_order': 600, 'image': None, 'label': '600.157.8b', 'multiplicity': 1, 'nt': [10, 17], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 8, 8, 0, 0, 0, 0, -2, -2, 3, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 3, 3, -2, -2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12743508
    {'cdim': 8, 'counter': 23, 'faithful': True, 'group': '600.157', 'group_order': 600, 'image': None, 'label': '600.157.8c', 'multiplicity': 2, 'nt': [30, 147], 'qdim': 16, 'qvalues': [16, 0, 0, 0, -8, -8, 0, 0, 0, 0, -4, -4, -4, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -3, -3, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12743509
    {'cdim': 8, 'counter': 24, 'faithful': True, 'group': '600.157', 'group_order': 600, 'image': None, 'label': '600.157.8d', 'multiplicity': 2, 'nt': [30, 147], 'qdim': 16, 'qvalues': [16, 0, 0, 0, -8, -8, 0, 0, 0, 0, -4, -4, 6, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -3, -3, 2, 2, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 29391451
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 600, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 600, 'label': '600.157.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 29391462
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 600, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 300, 'label': '600.157.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 29391473
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 600, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 300, 'label': '600.157.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 29391484
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 600, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 300, 'label': '600.157.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 29391488
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 600, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 200, 'label': '600.157.1e1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]]]}
  • id: 29391489
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 600, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 200, 'label': '600.157.1e2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]]]}
  • id: 29391490
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 600, 'counter': 7, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.b1', 'kernel_order': 150, 'label': '600.157.1f1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 29391491
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 600, 'counter': 8, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.b1', 'kernel_order': 150, 'label': '600.157.1f2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 29391492
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 600, 'counter': 9, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 150, 'label': '600.157.1g1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 29391452
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 600, 'counter': 10, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 150, 'label': '600.157.1g2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 29391453
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 600, 'counter': 11, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 100, 'label': '600.157.1h1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]]]}
  • id: 29391454
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 600, 'counter': 12, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 100, 'label': '600.157.1h2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]]]}
  • id: 29391455
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 600, 'counter': 13, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.a1', 'kernel_order': 100, 'label': '600.157.1i1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]]]}
  • id: 29391456
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 600, 'counter': 14, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.a1', 'kernel_order': 100, 'label': '600.157.1i2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]]]}
  • id: 29391457
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 600, 'counter': 15, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 100, 'label': '600.157.1j1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]]]}
  • id: 29391458
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 600, 'counter': 16, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 100, 'label': '600.157.1j2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]]]}
  • id: 29391459
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 600, 'counter': 17, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.b1', 'kernel_order': 50, 'label': '600.157.1k1', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[-1, 4]], [[-1, 2]], [[1, 4]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[1, 0]], [[1, 5]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 5]], [[-1, 1]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 2]], [[-1, 4]]]}
  • id: 29391460
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 600, 'counter': 18, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.b1', 'kernel_order': 50, 'label': '600.157.1k2', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 4]], [[-1, 2]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 4]], [[1, 2]], [[1, 4]], [[-1, 2]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[-1, 5]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 5]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[-1, 4]], [[1, 2]]]}
  • id: 29391461
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 600, 'counter': 19, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.b1', 'kernel_order': 50, 'label': '600.157.1k3', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 4]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[-1, 4]], [[-1, 2]], [[1, 4]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[1, 0]], [[-1, 5]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 5]], [[1, 1]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 2]], [[-1, 4]]]}
  • id: 29391463
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 600, 'counter': 20, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.b1', 'kernel_order': 50, 'label': '600.157.1k4', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 4]], [[-1, 2]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 4]], [[1, 2]], [[1, 4]], [[-1, 2]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, 5]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 5]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[-1, 4]], [[1, 2]]]}
  • id: 29391464
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 600, 'counter': 21, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.a1', 'kernel_order': 50, 'label': '600.157.1l1', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 0]], [[-1, 0]], [[-1, 5]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 1]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 2]], [[-1, 4]], [[-1, 2]], [[1, 4]]]}
  • id: 29391465
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 600, 'counter': 22, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.a1', 'kernel_order': 50, 'label': '600.157.1l2', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 4]], [[-1, 2]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 5]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[-1, 4]], [[1, 2]], [[1, 4]], [[-1, 2]]]}
  • id: 29391466
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 600, 'counter': 23, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.a1', 'kernel_order': 50, 'label': '600.157.1l3', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2]], [[1, 4]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 0]], [[-1, 0]], [[1, 5]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[1, 1]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 2]], [[-1, 4]], [[-1, 2]], [[1, 4]]]}
  • id: 29391467
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 600, 'counter': 24, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.a1', 'kernel_order': 50, 'label': '600.157.1l4', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 4]], [[-1, 2]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 5]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[-1, 4]], [[1, 2]], [[1, 4]], [[-1, 2]]]}
  • id: 29391468
    {'center': '20.a1.b1', 'center_index': 20, 'center_order': 30, 'counter': 25, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '20.3', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.b1', 'kernel_order': 30, 'label': '600.157.4a', 'nt': [5, 3], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 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]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29391469
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 30, 'counter': 26, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '20.3', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.a1', 'kernel_order': 30, 'label': '600.157.4b', 'nt': [5, 3], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[4, 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]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 29391470
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 30, 'counter': 27, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '40.12', 'image_order': 40, 'indicator': 1, 'kernel': '40.a1.b1', 'kernel_order': 15, 'label': '600.157.4c', 'nt': [10, 5], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[-4, 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]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 29391471
    {'center': '20.a1.b1', 'center_index': 20, 'center_order': 30, 'counter': 28, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '40.12', 'image_order': 40, 'indicator': 1, 'kernel': '40.a1.a1', 'kernel_order': 15, 'label': '600.157.4d', 'nt': [10, 5], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 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]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29391472
    {'center': '20.a1.b1', 'center_index': 20, 'center_order': 30, 'counter': 29, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '60.6', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.b1', 'kernel_order': 10, 'label': '600.157.4e1', 'nt': [15, 8], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[4, 1]], [[4, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]]]}
  • id: 29391474
    {'center': '20.a1.b1', 'center_index': 20, 'center_order': 30, 'counter': 30, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '60.6', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.b1', 'kernel_order': 10, 'label': '600.157.4e2', 'nt': [15, 2], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[4, -1]], [[4, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 29391475
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 30, 'counter': 31, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '60.6', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.a1', 'kernel_order': 10, 'label': '600.157.4f1', 'nt': [15, 8], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[4, -1]], [[4, 1]], [[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]], [[4, 1]], [[4, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]]]}
  • id: 29391476
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 30, 'counter': 32, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '60.6', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.a1', 'kernel_order': 10, 'label': '600.157.4f2', 'nt': [15, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[4, 1]], [[4, -1]], [[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]], [[4, -1]], [[4, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]]]}
  • id: 29391477
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 30, 'counter': 33, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '120.40', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.b1', 'kernel_order': 5, 'label': '600.157.4g1', 'nt': [30, 26], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-4, -1]], [[-4, 1]], [[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]], [[4, 1]], [[4, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]]]}
  • id: 29391478
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 30, 'counter': 34, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '120.40', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.b1', 'kernel_order': 5, 'label': '600.157.4g2', 'nt': [30, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-4, 1]], [[-4, -1]], [[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]], [[4, -1]], [[4, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]]]}
  • id: 29391479
    {'center': '20.a1.b1', 'center_index': 20, 'center_order': 30, 'counter': 35, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '120.40', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 5, 'label': '600.157.4h1', 'nt': [30, 26], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-4, -1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[4, 1]], [[4, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]]]}
  • id: 29391480
    {'center': '20.a1.b1', 'center_index': 20, 'center_order': 30, 'counter': 36, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '120.40', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 5, 'label': '600.157.4h2', 'nt': [30, 2], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-4, 1]], [[-4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[4, -1]], [[4, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 29391481
    {'center': '200.a1.a1', 'center_index': 200, 'center_order': 3, 'counter': 37, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '200.42', 'image_order': 200, 'indicator': 1, 'kernel': '200.a1.a1', 'kernel_order': 3, 'label': '600.157.8a', 'nt': [10, 17], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29391482
    {'center': '200.a1.a1', 'center_index': 200, 'center_order': 3, 'counter': 38, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '200.42', 'image_order': 200, 'indicator': 1, 'kernel': '200.a1.a1', 'kernel_order': 3, 'label': '600.157.8b', 'nt': [10, 17], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[3, 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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29391483
    {'center': '200.a1.a1', 'center_index': 200, 'center_order': 3, 'counter': 39, 'cyclotomic_n': 3, 'dim': 8, 'faithful': True, 'field': [1, -1, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '600.157', 'image_order': 600, 'indicator': 0, 'kernel': '600.a1.a1', 'kernel_order': 1, 'label': '600.157.8c1', 'nt': [30, 147], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, -1]], [[8, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 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]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29391485
    {'center': '200.a1.a1', 'center_index': 200, 'center_order': 3, 'counter': 40, 'cyclotomic_n': 3, 'dim': 8, 'faithful': True, 'field': [1, -1, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '600.157', 'image_order': 600, 'indicator': 0, 'kernel': '600.a1.a1', 'kernel_order': 1, 'label': '600.157.8c2', 'nt': [30, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 1]], [[8, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 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]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29391486
    {'center': '200.a1.a1', 'center_index': 200, 'center_order': 3, 'counter': 41, 'cyclotomic_n': 3, 'dim': 8, 'faithful': True, 'field': [1, -1, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '600.157', 'image_order': 600, 'indicator': 0, 'kernel': '600.a1.a1', 'kernel_order': 1, 'label': '600.157.8d1', 'nt': [30, 147], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, -1]], [[8, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[3, 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, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[3, 1]], [[3, -1]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29391487
    {'center': '200.a1.a1', 'center_index': 200, 'center_order': 3, 'counter': 42, 'cyclotomic_n': 3, 'dim': 8, 'faithful': True, 'field': [1, -1, 1], 'group': '600.157', 'group_counter': 157, 'group_order': 600, 'image': None, 'image_isoclass': '600.157', 'image_order': 600, 'indicator': 0, 'kernel': '600.a1.a1', 'kernel_order': 1, 'label': '600.157.8d2', 'nt': [30, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 1]], [[8, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[3, 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, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[3, -1]], [[3, 1]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

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

  
  
  • id: 110305756
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 600, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '600.157.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '600.157', 'subgroup_hash': 157, 'subgroup_order': 600, 'subgroup_tex': 'D_5^2.C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110305767
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 300, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '600.157.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '300.36', 'subgroup_hash': 36, 'subgroup_order': 300, 'subgroup_tex': 'C_3\\times D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 110305778
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 300, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '600.157.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '300.30', 'subgroup_hash': 30, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305789
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 300, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '600.157.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '300.31', 'subgroup_hash': 31, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305800
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': True, 'centralizer_order': 3, 'characteristic': True, 'core_order': 200, 'counter': 5, 'cyclic': False, 'direct': True, 'hall': 10, 'label': '600.157.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '200.42', 'subgroup_hash': 42, 'subgroup_order': 200, 'subgroup_tex': 'D_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305811
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 150, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '600.157.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '150.8', 'subgroup_hash': 8, 'subgroup_order': 150, 'subgroup_tex': 'D_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 110305822
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 150, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '600.157.4.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '150.8', 'subgroup_hash': 8, 'subgroup_order': 150, 'subgroup_tex': 'D_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 110305830
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 150, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '600.157.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305831
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 30, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.5.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.40', 'subgroup_hash': 40, 'subgroup_order': 120, 'subgroup_tex': 'C_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305757
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 30, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.5.a1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110305758
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 100, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '600.157.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '100.13', 'subgroup_hash': 13, 'subgroup_order': 100, 'subgroup_tex': 'D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 110305759
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 100, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '600.157.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '100.11', 'subgroup_hash': 11, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305760
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 100, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '600.157.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '100.12', 'subgroup_hash': 12, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305761
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': True, 'core_order': 75, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 15, 'label': '600.157.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['F', 'S', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 110305762
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 30, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110305763
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 30, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.10.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110305764
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 15, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.10.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305765
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 15, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.10.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110305766
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.10.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305768
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.10.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305769
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 15, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.10.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305770
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 15, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.10.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305771
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 50, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '600.157.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305772
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 50, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '600.157.12.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305773
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 50, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '600.157.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305774
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 10, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.15.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305775
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 10, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.15.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110305776
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 30, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '600.157.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305777
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 30, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '600.157.20.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305779
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 15, 'counter': 30, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '600.157.20.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '20.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 110305780
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 15, 'counter': 31, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '600.157.20.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '20.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110305781
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 15, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.20.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305782
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 15, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.20.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110305783
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.20.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305784
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.20.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305785
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': True, 'core_order': 25, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 5, 'label': '600.157.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{12}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '25.2', 'subgroup_hash': 2, 'subgroup_order': 25, 'subgroup_tex': 'C_5^2', 'supersolvable': True, 'sylow': 5}
  • id: 110305786
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '600.157.25.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '25.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 25, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110305787
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 10, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.30.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110305788
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 10, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.30.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110305790
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.30.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305791
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.30.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305792
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.30.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305793
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.30.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110305794
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.30.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305795
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.30.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110305796
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 15, 'counter': 46, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '600.157.40.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 110305797
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 15, 'counter': 47, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '600.157.40.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times F_5', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 110305798
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 3, 'counter': 48, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '600.157.40.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 110305799
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 3, 'counter': 49, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '600.157.40.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 110305801
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.50.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '50.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 50, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110305802
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 51, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '600.157.50.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '50.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 50, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110305803
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 52, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '600.157.50.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '50.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 50, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110305804
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 10, 'counter': 53, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '600.157.60.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '60.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.6', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305805
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 10, 'counter': 54, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '600.157.60.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '60.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.6', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305806
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 5, 'counter': 55, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '600.157.60.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110305807
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 5, 'counter': 56, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '600.157.60.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110305808
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.60.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305809
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.60.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305810
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.60.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305812
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.60.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305813
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '600.157.75.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '75.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 75, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 2}
  • id: 110305814
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 3, 'counter': 62, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '600.157.100.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110305815
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 3, 'counter': 63, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '600.157.100.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110305816
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 64, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '600.157.100.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110305817
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 5, 'counter': 65, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '600.157.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '120.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.40', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 40, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times F_5', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305818
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 5, 'counter': 66, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '600.157.120.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '120.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.40', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 40, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times F_5', 'simple': True, 'solvable': True, 'special_labels': ['C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305819
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 67, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '600.157.120.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305820
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 68, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '600.157.120.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
  • id: 110305821
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '600.157.150.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '150.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110305823
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 70, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '600.157.150.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '150.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110305824
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 71, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '600.157.150.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '150.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110305825
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': True, 'central_factor': False, 'centralizer_order': 600, 'characteristic': True, 'core_order': 3, 'counter': 72, 'cyclic': True, 'direct': True, 'hall': 3, 'label': '600.157.200.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '200.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '200.42', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 42, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 200, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_5:F_5', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
  • id: 110305826
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 73, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '600.157.300.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '300.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 110305827
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 74, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '600.157.300.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '300.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 110305828
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 75, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '600.157.300.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '300.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 110305829
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '600.157', 'ambient_counter': 157, 'ambient_order': 600, 'ambient_tex': 'D_5^2.C_6', 'central': True, 'central_factor': False, 'centralizer_order': 600, 'characteristic': True, 'core_order': 1, 'counter': 76, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '600.157.600.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '600.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '600.157', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 157, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 600, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_5^2.C_6', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'PC', 'U1', 'D2', 'C6'], '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: 110305756
    {'ambient': '600.157', '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': '200.a1.a1', 'complements': ['600.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '3.a1.a1', '5.a1.a1', '5.a1.b1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6589, 7142, 6604, 2807, 5696, 5750, 6297, 7021], 'generators': [1, 120, 400, 2, 20, 8], 'label': '600.157.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.c1.a1', '2.b1.a1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110305757
    {'ambient': '600.157', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '40.12', 'aut_weyl_index': 40, 'centralizer': '100.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.b1', '10.b1.b1', '10.d1.b1', '15.a1.b1', '25.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [7623, -1, 6790, -1, 6374, -1, 6056, -1], 'generators': [1, 400, 2, 20, 120], 'label': '600.157.5.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '5.a1.b1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5.a1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305758
    {'ambient': '600.157', 'aut_centralizer_order': 2, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 2, 'centralizer': '200.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.a1.b1', '12.b1.a1', '30.a1.a1', '30.a1.b1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3210, 6075, 2859, 3990, 2603, 6142, 4072, 5080], 'generators': [2, 8, 120, 20], 'label': '600.157.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '12.a1.b1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110305759
    {'ambient': '600.157', 'aut_centralizer_order': 2, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 2, 'centralizer': '200.a1.a1', 'complements': ['100.a1.a1', '100.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '30.b1.a1', '30.b1.b1', '30.c1.a1', '30.c1.b1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8733, 7569, 8724, 1251, 7142, 7741, 9829, 8736], 'generators': [1, 8, 120, 2], 'label': '600.157.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.b1.a1', '3.a1.a1'], 'normal_contains': ['12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '600.157', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110305760
    {'ambient': '600.157', 'aut_centralizer_order': 2, 'aut_label': '6.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 2, 'centralizer': '200.a1.a1', 'complements': ['100.a1.a1', '100.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '30.d1.a1', '30.d1.b1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5380, 9123, 5538, 2401, 4929, 9405, 5959, 7689], 'generators': [5, 8, 120, 34], 'label': '600.157.6.c1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.c1.a1', 'normal_contained_in': ['2.c1.a1', '3.a1.a1'], 'normal_contains': ['12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '600.157', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110305761
    {'ambient': '600.157', 'aut_centralizer_order': 25, 'aut_label': '8.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '64.101', 'aut_weyl_index': 25, 'centralizer': '8.a1.a1', 'complements': ['75.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.a1.b1', '4.b1.a1'], 'contains': ['24.a1.a1', '40.a1.a1', '40.a1.b1', '40.b1.a1', '40.b1.b1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1987, 3026, 2003, 7440, 2591, 3418, 2380, 3559], 'generators': [400, 120, 8], 'label': '600.157.8.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.a1.b1', '4.b1.a1'], 'normal_contains': ['24.a1.a1', '40.a1.a1', '40.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '200.42', 'quotient_action_image': '8.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 110305762
    {'ambient': '600.157', 'aut_centralizer_order': 4, 'aut_label': '10.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '40.12', 'aut_weyl_index': 40, 'centralizer': '100.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['20.a1.b1', '20.b1.a1', '20.c1.a1', '30.a1.a1', '50.a1.a1'], 'core': '20.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [3573, -1, 4659, -1, 3257, -1, 3676, -1], 'generators': [2, 400, 8, 20], 'label': '600.157.10.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305763
    {'ambient': '600.157', 'aut_centralizer_order': 4, 'aut_label': '10.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '40.12', 'aut_weyl_index': 40, 'centralizer': '100.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.b1'], 'contains': ['20.a1.a1', '20.b1.b1', '20.c1.b1', '30.a1.b1', '50.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3573, -1, 3633, -1, 3257, -1, 3183, -1], 'generators': [2, 400, 120, 20], 'label': '600.157.10.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '10.a1.b1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.a1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305764
    {'ambient': '600.157', 'aut_centralizer_order': 4, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '40.12', 'aut_weyl_index': 40, 'centralizer': '100.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.a1'], 'contains': ['20.c1.a1', '30.b1.a1', '50.b1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [8087, -1, 8664, -1, 8849, -1, 8410, -1], 'generators': [1, 2, 8, 400], 'label': '600.157.10.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.b1.a1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305765
    {'ambient': '600.157', 'aut_centralizer_order': 4, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '40.12', 'aut_weyl_index': 40, 'centralizer': '100.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.b1'], 'contains': ['20.c1.b1', '30.b1.b1', '50.b1.a1'], 'core': '40.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [8087, -1, 7801, -1, 8849, -1, 7924, -1], 'generators': [1, 2, 120, 400], 'label': '600.157.10.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '10.b1.b1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.b1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305766
    {'ambient': '600.157', 'aut_centralizer_order': 2, 'aut_label': '10.c1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '40.12', 'aut_weyl_index': 40, 'centralizer': '200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['20.d1.a1', '30.c1.a1', '50.b1.a1'], 'core': '200.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [9831, -1, 9861, -1, 9652, -1, 8896, -1], 'generators': [1, 2, 248, 400], 'label': '600.157.10.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.c1.a1', 'old_label': '10.c1.a1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.c1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305767
    {'ambient': '600.157', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1600.10254', 'aut_weyl_index': 1, 'centralizer': '200.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.a1.b1', '4.b1.a1', '6.a1.a1', '10.a1.a1', '10.a1.b1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3592, 3149, 3673, 5208, 3257, 1493, 3676, 4700], 'generators': [2, 400, 8, 20, 120], 'label': '600.157.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.a1.b1', '4.b1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110305768
    {'ambient': '600.157', 'aut_centralizer_order': 2, 'aut_label': '10.c1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '40.12', 'aut_weyl_index': 40, 'centralizer': '200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['20.d1.b1', '30.c1.b1', '50.b1.a1'], 'core': '200.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [9831, -1, 9405, -1, 9652, -1, 9383, -1], 'generators': [1, 2, 128, 400], 'label': '600.157.10.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.c1.b1', 'old_label': '10.c1.b1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.c1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305769
    {'ambient': '600.157', 'aut_centralizer_order': 4, 'aut_label': '10.d1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '40.12', 'aut_weyl_index': 40, 'centralizer': '100.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '5.a1.a1'], 'contains': ['20.c1.a1', '30.d1.a1', '50.c1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [6044, -1, 7084, -1, 5601, -1, 5552, -1], 'generators': [5, 34, 8, 400], 'label': '600.157.10.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.d1.a1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.d1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305770
    {'ambient': '600.157', 'aut_centralizer_order': 4, 'aut_label': '10.d1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '40.12', 'aut_weyl_index': 40, 'centralizer': '100.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '5.a1.b1'], 'contains': ['20.c1.b1', '30.d1.b1', '50.c1.a1'], 'core': '40.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [6044, -1, 5650, -1, 5601, -1, 5066, -1], 'generators': [5, 34, 120, 400], 'label': '600.157.10.d1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '10.d1.b1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.d1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305771
    {'ambient': '600.157', 'aut_centralizer_order': 10, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '80.30', 'aut_weyl_index': 20, 'centralizer': '40.a1.a1', 'complements': ['50.b1.a1', '50.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1'], 'contains': ['24.a1.a1', '60.a1.a1', '60.b1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [640, 3757, 727, 5242, 354, 5865, 2920, 6507], 'generators': [20, 120, 8], 'label': '600.157.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '600.157', 'quotient_action_image': '4.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 110305772
    {'ambient': '600.157', 'aut_centralizer_order': 10, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '80.30', 'aut_weyl_index': 20, 'centralizer': '40.a1.b1', 'complements': ['50.b1.a1', '50.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '6.a1.a1'], 'contains': ['24.a1.a1', '60.a1.b1', '60.b1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [640, 3757, 2019, 3697, 354, 5865, 1026, 2018], 'generators': [38, 8, 120], 'label': '600.157.12.a1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': ['4.a1.b1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '60.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.b1', 'projective_image': '600.157', 'quotient_action_image': '4.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.a1.b1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 110305773
    {'ambient': '600.157', 'aut_centralizer_order': 2, 'aut_label': '12.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 2, 'centralizer': '200.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1', '6.b1.a1', '6.c1.a1'], 'contains': ['24.a1.a1', '60.c1.a1', '60.c1.b1', '60.d1.a1', '60.d1.b1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4382, 6090, 3613, 2401, 3882, 7741, 6441, 7689], 'generators': [2, 120, 8], 'label': '600.157.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1', '6.c1.a1', '6.b1.a1'], 'normal_contains': ['24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110305774
    {'ambient': '600.157', 'aut_centralizer_order': 8, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '20.3', 'aut_weyl_index': 80, 'centralizer': '100.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '5.a1.a1'], 'contains': ['30.a1.a1', '30.b1.a1', '30.d1.a1', '75.a1.a1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [7260, -1, 6956, -1, 6404, -1, 7438, -1], 'generators': [1, 2, 8, 20], 'label': '600.157.15.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '15.a1.a1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305775
    {'ambient': '600.157', 'aut_centralizer_order': 8, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '20.3', 'aut_weyl_index': 80, 'centralizer': '100.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '5.a1.b1'], 'contains': ['30.a1.b1', '30.b1.b1', '30.d1.b1', '75.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [7260, -1, 6239, -1, 6404, -1, 6952, -1], 'generators': [1, 2, 120, 20], 'label': '600.157.15.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '15.a1.b1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.a1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305776
    {'ambient': '600.157', 'aut_centralizer_order': 20, 'aut_label': '20.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '40.12', 'aut_weyl_index': 40, 'centralizer': '20.a1.b1', 'complements': ['30.b1.a1', '30.c1.b1', '30.c1.a1', '30.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.b1'], 'contains': ['40.a1.b1', '60.a1.a1', '100.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [878, 906, 944, 9041, 1698, 971, 1519, 5100], 'generators': [20, 120, 400], 'label': '600.157.20.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['40.a1.b1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '200.42', 'quotient_action_image': '4.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '20.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305777
    {'ambient': '600.157', 'aut_centralizer_order': 20, 'aut_label': '20.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '40.12', 'aut_weyl_index': 40, 'centralizer': '20.a1.a1', 'complements': ['30.b1.b1', '30.c1.b1', '30.c1.a1', '30.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '10.a1.a1'], 'contains': ['40.a1.a1', '60.a1.b1', '100.a1.b1'], 'core': '20.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [878, 906, 2743, 6628, 1698, 971, 533, 611], 'generators': [38, 8, 400], 'label': '600.157.20.a1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '20.a1.b1', 'normal_contained_in': ['4.a1.b1'], 'normal_contains': ['40.a1.a1', '60.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.b1', 'projective_image': '200.42', 'quotient_action_image': '4.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '20.a1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305778
    {'ambient': '600.157', 'aut_centralizer_order': 1, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1600.10254', 'aut_weyl_index': 1, 'centralizer': '200.a1.a1', 'complements': ['300.a1.a1', '300.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '6.b1.a1', '10.b1.a1', '10.b1.b1', '10.c1.a1', '10.c1.b1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8495, 5785, 8724, 959, 7338, 4315, 8410, 9127], 'generators': [1, 2, 8, 400, 120], 'label': '600.157.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '6.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '200.42', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110305779
    {'ambient': '600.157', 'aut_centralizer_order': 20, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '8.2', 'aut_weyl_index': 200, 'centralizer': '20.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.a1'], 'contains': ['40.a1.a1', '60.b1.a1', '100.a1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [2539, -1, 2013, -1, 1026, -1, 1926, -1], 'generators': [20, 8, 400], 'label': '600.157.20.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.b1.a1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 110305780
    {'ambient': '600.157', 'aut_centralizer_order': 20, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '8.2', 'aut_weyl_index': 200, 'centralizer': '20.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '10.a1.b1'], 'contains': ['40.a1.b1', '60.b1.b1', '100.a1.b1'], 'core': '40.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [2539, -1, 1583, -1, 1026, -1, 126, -1], 'generators': [38, 120, 400], 'label': '600.157.20.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '20.b1.b1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 110305781
    {'ambient': '600.157', 'aut_centralizer_order': 4, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '40.12', 'aut_weyl_index': 40, 'centralizer': '100.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '10.a1.a1', '10.b1.a1', '10.d1.a1'], 'contains': ['40.a1.a1', '60.c1.a1', '100.b1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4765, -1, 5132, -1, 4566, -1, 5040, -1], 'generators': [2, 8, 400], 'label': '600.157.20.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.c1.a1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.c1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305782
    {'ambient': '600.157', 'aut_centralizer_order': 4, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '40.12', 'aut_weyl_index': 40, 'centralizer': '100.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '10.a1.b1', '10.b1.b1', '10.d1.b1'], 'contains': ['40.a1.b1', '60.c1.b1', '100.b1.a1'], 'core': '40.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [4765, -1, 4408, -1, 4566, -1, 4547, -1], 'generators': [2, 120, 400], 'label': '600.157.20.c1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '20.c1.b1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.c1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305783
    {'ambient': '600.157', 'aut_centralizer_order': 2, 'aut_label': '20.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '40.12', 'aut_weyl_index': 40, 'centralizer': '200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '10.c1.a1'], 'contains': ['40.b1.a1', '60.d1.a1', '100.b1.a1'], 'core': '200.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6821, -1, 7609, -1, 6196, -1, 5534, -1], 'generators': [2, 248, 400], 'label': '600.157.20.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.c1.a1', 'old_label': '20.d1.a1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.d1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305784
    {'ambient': '600.157', 'aut_centralizer_order': 2, 'aut_label': '20.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '40.12', 'aut_weyl_index': 40, 'centralizer': '200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '10.c1.b1'], 'contains': ['40.b1.b1', '60.d1.b1', '100.b1.a1'], 'core': '200.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6821, -1, 6756, -1, 6196, -1, 6027, -1], 'generators': [2, 128, 400], 'label': '600.157.20.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.c1.b1', 'old_label': '20.d1.b1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.d1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305785
    {'ambient': '600.157', 'aut_centralizer_order': 50, 'aut_label': '24.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '32.11', 'aut_weyl_index': 50, 'centralizer': '8.a1.a1', 'complements': ['25.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.a1.b1', '12.b1.a1'], 'contains': ['120.a1.a1', '120.a1.b1', '120.b1.a1', '120.b1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1843, 4917, 108, 4373, 2591, 5865, 3860, 3631], 'generators': [8, 120], 'label': '600.157.24.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1', '12.a1.b1', '12.b1.a1'], 'normal_contains': ['120.a1.a1', '120.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '600.157', 'quotient_action_image': '8.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 110305786
    {'ambient': '600.157', 'aut_centralizer_order': 16, 'aut_label': '25.a1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '4.2', 'aut_weyl_index': 400, 'centralizer': '25.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '5.a1.b1'], 'contains': ['50.a1.a1', '50.b1.a1', '50.c1.a1', '75.a1.a1'], 'core': '200.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [8783, -1, 8678, -1, 7962, -1, 6416, -1], 'generators': [1, 20, 400, 2], 'label': '600.157.25.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '25.a1.a1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '25.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110305787
    {'ambient': '600.157', 'aut_centralizer_order': 8, 'aut_label': '30.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '20.3', 'aut_weyl_index': 80, 'centralizer': '100.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.a1.a1', '15.a1.a1'], 'contains': ['60.a1.b1', '60.b1.a1', '60.c1.a1', '150.a1.a1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [3172, -1, 4280, -1, 3340, -1, 4140, -1], 'generators': [2, 8, 20], 'label': '600.157.30.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '30.a1.a1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305788
    {'ambient': '600.157', 'aut_centralizer_order': 8, 'aut_label': '30.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '20.3', 'aut_weyl_index': 80, 'centralizer': '100.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.a1.b1', '15.a1.b1'], 'contains': ['60.a1.a1', '60.b1.b1', '60.c1.b1', '150.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3172, -1, 3386, -1, 3340, -1, 3820, -1], 'generators': [2, 120, 20], 'label': '600.157.30.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '30.a1.b1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.a1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305789
    {'ambient': '600.157', 'aut_centralizer_order': 1, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1600.10254', 'aut_weyl_index': 1, 'centralizer': '200.a1.a1', 'complements': ['300.a1.a1', '300.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '6.c1.a1', '10.d1.a1', '10.d1.b1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5830, 8483, 5924, 3382, 4929, 7202, 5512, 6364], 'generators': [5, 34, 8, 400, 120], 'label': '600.157.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '6.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '200.42', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110305790
    {'ambient': '600.157', 'aut_centralizer_order': 8, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '20.3', 'aut_weyl_index': 80, 'centralizer': '100.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '10.b1.a1', '15.a1.a1'], 'contains': ['60.c1.a1', '150.b1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [7542, -1, 7994, -1, 8581, -1, 8637, -1], 'generators': [1, 8, 2], 'label': '600.157.30.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '30.b1.a1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305791
    {'ambient': '600.157', 'aut_centralizer_order': 8, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '20.3', 'aut_weyl_index': 80, 'centralizer': '100.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '10.b1.b1', '15.a1.b1'], 'contains': ['60.c1.b1', '150.b1.a1'], 'core': '120.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [7542, -1, 7751, -1, 8581, -1, 8378, -1], 'generators': [1, 120, 2], 'label': '600.157.30.b1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '30.b1.b1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305792
    {'ambient': '600.157', 'aut_centralizer_order': 4, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '20.3', 'aut_weyl_index': 80, 'centralizer': '200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '10.c1.a1'], 'contains': ['60.d1.a1', '150.b1.a1'], 'core': '600.a1.a1', 'coset_action_label': '30T147', 'count': 10, 'diagramx': [9774, -1, 9892, -1, 9010, -1, 8896, -1], 'generators': [1, 248, 2], 'label': '600.157.30.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.c1.a1', 'old_label': '30.c1.a1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.c1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305793
    {'ambient': '600.157', 'aut_centralizer_order': 4, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '20.3', 'aut_weyl_index': 80, 'centralizer': '200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '10.c1.b1'], 'contains': ['60.d1.b1', '150.b1.a1'], 'core': '600.a1.a1', 'coset_action_label': '30T147', 'count': 10, 'diagramx': [9774, -1, 9341, -1, 9010, -1, 9267, -1], 'generators': [1, 128, 2], 'label': '600.157.30.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.c1.b1', 'old_label': '30.c1.b1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.c1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305794
    {'ambient': '600.157', 'aut_centralizer_order': 8, 'aut_label': '30.d1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '20.3', 'aut_weyl_index': 80, 'centralizer': '100.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '10.d1.a1', '15.a1.a1'], 'contains': ['60.c1.a1', '150.c1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5555, -1, 6205, -1, 6821, -1, 7312, -1], 'generators': [5, 8, 34], 'label': '600.157.30.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '30.d1.a1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.d1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305795
    {'ambient': '600.157', 'aut_centralizer_order': 8, 'aut_label': '30.d1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '20.3', 'aut_weyl_index': 80, 'centralizer': '100.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '10.d1.b1', '15.a1.b1'], 'contains': ['60.c1.b1', '150.c1.a1'], 'core': '120.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [5555, -1, 5674, -1, 6821, -1, 7053, -1], 'generators': [5, 120, 34], 'label': '600.157.30.d1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '30.d1.b1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.d1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305796
    {'ambient': '600.157', 'aut_centralizer_order': 100, 'aut_label': '40.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '8.2', 'aut_weyl_index': 200, 'centralizer': '4.a1.a1', 'complements': ['15.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '20.a1.b1', '20.b1.a1', '20.c1.a1'], 'contains': ['120.a1.a1', '200.a1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1624, 877, 1969, 7068, 3096, 3303, 2344, 2758], 'generators': [400, 8], 'label': '600.157.40.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': ['8.a1.a1', '20.a1.b1'], 'normal_contains': ['120.a1.a1', '200.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.a1.a1', 'projective_image': '200.42', 'quotient_action_image': '4.1', 'quotient_action_kernel': '10.1', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '40.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 110305797
    {'ambient': '600.157', 'aut_centralizer_order': 100, 'aut_label': '40.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '8.2', 'aut_weyl_index': 200, 'centralizer': '4.a1.b1', 'complements': ['15.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '20.a1.a1', '20.b1.b1', '20.c1.b1'], 'contains': ['120.a1.b1', '200.a1.a1'], 'core': '40.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1624, 877, 900, 9041, 3096, 3303, 1768, 4504], 'generators': [400, 120], 'label': '600.157.40.a1.b1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '40.a1.b1', 'normal_contained_in': ['8.a1.a1', '20.a1.a1'], 'normal_contains': ['120.a1.b1', '200.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.a1.b1', 'projective_image': '200.42', 'quotient_action_image': '4.1', 'quotient_action_kernel': '10.1', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '40.a1.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 110305798
    {'ambient': '600.157', 'aut_centralizer_order': 50, 'aut_label': '40.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 200, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '20.d1.a1'], 'contains': ['120.b1.a1', '200.a1.a1'], 'core': '200.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3843, -1, 3593, -1, 4048, -1, 3237, -1], 'generators': [400, 248], 'label': '600.157.40.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '40.b1.a1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 110305799
    {'ambient': '600.157', 'aut_centralizer_order': 50, 'aut_label': '40.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 200, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '20.d1.b1'], 'contains': ['120.b1.b1', '200.a1.a1'], 'core': '200.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3843, -1, 2652, -1, 4048, -1, 3554, -1], 'generators': [400, 128], 'label': '600.157.40.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '40.b1.b1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 110305800
    {'ambient': '600.157', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 2, 'centralizer': '200.a1.a1', 'complements': ['200.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '15.a1.a1', '15.a1.b1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6589, 8301, 6289, 1872, 5696, 9307, 6952, 7689], 'generators': [1, 2, 8, 20, 120], 'label': '600.157.3.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '6.c1.a1', '6.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '600.157', 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110305801
    {'ambient': '600.157', 'aut_centralizer_order': 16, 'aut_label': '50.a1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '4.2', 'aut_weyl_index': 400, 'centralizer': '25.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '10.a1.b1', '25.a1.a1'], 'contains': ['100.a1.a1', '100.a1.b1', '100.b1.a1', '150.a1.a1'], 'core': '200.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [5479, -1, 5088, -1, 5381, -1, 3413, -1], 'generators': [2, 20, 400], 'label': '600.157.50.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '50.a1.a1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110305802
    {'ambient': '600.157', 'aut_centralizer_order': 32, 'aut_label': '50.b1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '2.1', 'aut_weyl_index': 800, 'centralizer': '25.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1', '10.b1.b1', '10.c1.a1', '10.c1.b1', '25.a1.a1'], 'contains': ['100.b1.a1', '150.b1.a1'], 'core': '200.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [9417, -1, 9019, -1, 9486, -1, 8090, -1], 'generators': [1, 400, 2], 'label': '600.157.50.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '50.b1.a1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110305803
    {'ambient': '600.157', 'aut_centralizer_order': 16, 'aut_label': '50.c1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '4.2', 'aut_weyl_index': 400, 'centralizer': '25.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.d1.a1', '10.d1.b1', '25.a1.a1'], 'contains': ['100.b1.a1', '150.c1.a1'], 'core': '200.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [8113, -1, 7263, -1, 7296, -1, 6765, -1], 'generators': [5, 400, 34], 'label': '600.157.50.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '50.c1.a1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110305804
    {'ambient': '600.157', 'aut_centralizer_order': 40, 'aut_label': '60.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '20.3', 'aut_weyl_index': 80, 'centralizer': '20.a1.b1', 'complements': ['10.b1.a1', '10.c1.b1', '10.c1.a1', '10.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '20.a1.a1', '30.a1.b1'], 'contains': ['120.a1.b1', '300.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [169, 2294, 470, 6493, 2133, 4608, 2632, 5326], 'generators': [20, 120], 'label': '600.157.60.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': ['12.a1.a1', '20.a1.a1'], 'normal_contains': ['120.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.a1', 'projective_image': '600.157', 'quotient_action_image': '4.1', 'quotient_action_kernel': '15.1', 'quotient_action_kernel_order': 15, 'quotient_fusion': None, 'short_label': '60.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305805
    {'ambient': '600.157', 'aut_centralizer_order': 40, 'aut_label': '60.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '20.3', 'aut_weyl_index': 80, 'centralizer': '20.a1.a1', 'complements': ['10.b1.b1', '10.c1.b1', '10.c1.a1', '10.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '20.a1.b1', '30.a1.a1'], 'contains': ['120.a1.a1', '300.a1.b1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [169, 2294, 2970, 4825, 2133, 4608, 1480, 1936], 'generators': [38, 8], 'label': '600.157.60.a1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': ['12.a1.b1', '20.a1.b1'], 'normal_contains': ['120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.b1', 'projective_image': '600.157', 'quotient_action_image': '4.1', 'quotient_action_kernel': '15.1', 'quotient_action_kernel_order': 15, 'quotient_fusion': None, 'short_label': '60.a1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305806
    {'ambient': '600.157', 'aut_centralizer_order': 40, 'aut_label': '60.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '4.1', 'aut_weyl_index': 400, 'centralizer': '20.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '20.b1.a1', '30.a1.a1'], 'contains': ['120.a1.a1', '300.a1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [1467, -1, 1543, -1, 1657, -1, 2920, -1], 'generators': [20, 8], 'label': '600.157.60.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '60.b1.a1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 110305807
    {'ambient': '600.157', 'aut_centralizer_order': 40, 'aut_label': '60.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '4.1', 'aut_weyl_index': 400, 'centralizer': '20.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '20.b1.b1', '30.a1.b1'], 'contains': ['120.a1.b1', '300.a1.b1'], 'core': '120.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [1467, -1, 1242, -1, 1657, -1, 1192, -1], 'generators': [38, 120], 'label': '600.157.60.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '60.b1.b1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 110305808
    {'ambient': '600.157', 'aut_centralizer_order': 8, 'aut_label': '60.c1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '20.3', 'aut_weyl_index': 80, 'centralizer': '100.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '20.c1.a1', '30.a1.a1', '30.b1.a1', '30.d1.a1'], 'contains': ['120.a1.a1', '300.b1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4220, -1, 5339, -1, 4566, -1, 5739, -1], 'generators': [2, 8], 'label': '600.157.60.c1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '60.c1.a1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.c1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305809
    {'ambient': '600.157', 'aut_centralizer_order': 8, 'aut_label': '60.c1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '20.3', 'aut_weyl_index': 80, 'centralizer': '100.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '20.c1.b1', '30.a1.b1', '30.b1.b1', '30.d1.b1'], 'contains': ['120.a1.b1', '300.b1.a1'], 'core': '120.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [4220, -1, 3829, -1, 4566, -1, 5480, -1], 'generators': [2, 120], 'label': '600.157.60.c1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '60.c1.b1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.c1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305810
    {'ambient': '600.157', 'aut_centralizer_order': 4, 'aut_label': '60.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '20.3', 'aut_weyl_index': 80, 'centralizer': '200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '20.d1.a1', '30.c1.a1'], 'contains': ['120.b1.a1', '300.b1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6846, -1, 7920, -1, 5625, -1, 5998, -1], 'generators': [2, 248], 'label': '600.157.60.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.c1.a1', 'old_label': '60.d1.a1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.d1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305811
    {'ambient': '600.157', 'aut_centralizer_order': 5, 'aut_label': '4.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '160.203', 'aut_weyl_index': 10, 'centralizer': '40.a1.a1', 'complements': ['150.b1.a1', '150.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '12.a1.a1', '20.a1.a1', '20.b1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1987, 1487, 1532, 7959, 1698, 1395, 2380, 3806], 'generators': [20, 8, 120, 400], 'label': '600.157.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '12.a1.a1', '20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '200.42', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 110305812
    {'ambient': '600.157', 'aut_centralizer_order': 4, 'aut_label': '60.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '20.3', 'aut_weyl_index': 80, 'centralizer': '200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '20.d1.b1', '30.c1.b1'], 'contains': ['120.b1.b1', '300.b1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6846, -1, 5711, -1, 5625, -1, 6258, -1], 'generators': [2, 128], 'label': '600.157.60.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.c1.b1', 'old_label': '60.d1.b1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.d1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110305813
    {'ambient': '600.157', 'aut_centralizer_order': 32, 'aut_label': '75.a1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '2.1', 'aut_weyl_index': 800, 'centralizer': '25.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1', '15.a1.b1', '25.a1.a1'], 'contains': ['150.a1.a1', '150.b1.a1', '150.c1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [7762, -1, 7183, -1, 7962, -1, 7687, -1], 'generators': [1, 20], 'label': '600.157.75.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '75.a1.a1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '75.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110305814
    {'ambient': '600.157', 'aut_centralizer_order': 80, 'aut_label': '100.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '2.1', 'aut_weyl_index': 800, 'centralizer': '5.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '20.b1.a1', '50.a1.a1'], 'contains': ['200.a1.a1', '300.a1.a1'], 'core': '200.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [2320, -1, 1685, -1, 3572, -1, 2056, -1], 'generators': [20, 400], 'label': '600.157.100.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '100.a1.a1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110305815
    {'ambient': '600.157', 'aut_centralizer_order': 80, 'aut_label': '100.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '2.1', 'aut_weyl_index': 800, 'centralizer': '5.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.b1', '20.b1.b1', '50.a1.a1'], 'contains': ['200.a1.a1', '300.a1.b1'], 'core': '200.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [2320, -1, 3136, -1, 3572, -1, 904, -1], 'generators': [38, 400], 'label': '600.157.100.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '100.a1.b1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110305816
    {'ambient': '600.157', 'aut_centralizer_order': 32, 'aut_label': '100.b1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '2.1', 'aut_weyl_index': 800, 'centralizer': '25.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.c1.a1', '20.c1.b1', '20.d1.a1', '20.d1.b1', '50.a1.a1', '50.b1.a1', '50.c1.a1'], 'contains': ['200.a1.a1', '300.b1.a1'], 'core': '200.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [6138, -1, 6319, -1, 6053, -1, 5221, -1], 'generators': [2, 400], 'label': '600.157.100.b1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '100.b1.a1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110305817
    {'ambient': '600.157', 'aut_centralizer_order': 200, 'aut_label': '120.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '4.1', 'aut_weyl_index': 400, 'centralizer': '4.a1.a1', 'complements': ['5.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '40.a1.a1', '60.a1.b1', '60.b1.a1', '60.c1.a1'], 'contains': ['600.a1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [633, 2005, 2094, 5253, 2680, 4576, 3150, 2892], 'generators': [8], 'label': '600.157.120.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': ['24.a1.a1', '40.a1.a1', '60.a1.b1'], 'normal_contains': ['600.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.a1.a1', 'projective_image': '600.157', 'quotient_action_image': '4.1', 'quotient_action_kernel': '30.2', 'quotient_action_kernel_order': 30, 'quotient_fusion': None, 'short_label': '120.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 110305818
    {'ambient': '600.157', 'aut_centralizer_order': 200, 'aut_label': '120.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '4.1', 'aut_weyl_index': 400, 'centralizer': '4.a1.b1', 'complements': ['5.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '40.a1.b1', '60.a1.a1', '60.b1.b1', '60.c1.b1'], 'contains': ['600.a1.a1'], 'core': '120.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [633, 2005, 433, 6493, 2680, 4576, 2632, 4463], 'generators': [120], 'label': '600.157.120.a1.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '120.a1.b1', 'normal_contained_in': ['24.a1.a1', '40.a1.b1', '60.a1.a1'], 'normal_contains': ['600.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.a1.b1', 'projective_image': '600.157', 'quotient_action_image': '4.1', 'quotient_action_kernel': '30.2', 'quotient_action_kernel_order': 30, 'quotient_fusion': None, 'short_label': '120.a1.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 110305819
    {'ambient': '600.157', 'aut_centralizer_order': 100, 'aut_label': '120.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.1', 'aut_weyl_index': 400, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '40.b1.a1', '60.d1.a1'], 'contains': ['600.a1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3799, -1, 3707, -1, 3620, -1, 3460, -1], 'generators': [248], 'label': '600.157.120.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '120.b1.a1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 110305820
    {'ambient': '600.157', 'aut_centralizer_order': 100, 'aut_label': '120.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.1', 'aut_weyl_index': 400, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '40.b1.b1', '60.d1.b1'], 'contains': ['600.a1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3799, -1, 2493, -1, 3620, -1, 3766, -1], 'generators': [128], 'label': '600.157.120.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '120.b1.b1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 110305821
    {'ambient': '600.157', 'aut_centralizer_order': 32, 'aut_label': '150.a1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '2.1', 'aut_weyl_index': 800, 'centralizer': '25.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '30.a1.b1', '50.a1.a1', '75.a1.a1'], 'contains': ['300.a1.a1', '300.a1.b1', '300.b1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [5310, -1, 4293, -1, 5166, -1, 4155, -1], 'generators': [2, 20], 'label': '600.157.150.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '150.a1.a1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110305822
    {'ambient': '600.157', 'aut_centralizer_order': 5, 'aut_label': '4.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '160.203', 'aut_weyl_index': 10, 'centralizer': '40.a1.b1', 'complements': ['150.b1.a1', '150.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '12.a1.b1', '20.a1.b1', '20.b1.b1'], 'core': '4.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1987, 1487, 2345, 6110, 1698, 1395, 1026, 2070], 'generators': [38, 120, 8, 400], 'label': '600.157.4.a1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.b1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '12.a1.b1', '20.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.b1', 'projective_image': '200.42', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.b1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 110305823
    {'ambient': '600.157', 'aut_centralizer_order': 64, 'aut_label': '150.b1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1600, 'centralizer': '25.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.b1.a1', '30.b1.b1', '30.c1.a1', '30.c1.b1', '50.b1.a1', '75.a1.a1'], 'contains': ['300.b1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [8546, -1, 8248, -1, 8581, -1, 8378, -1], 'generators': [1], 'label': '600.157.150.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '150.b1.a1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110305824
    {'ambient': '600.157', 'aut_centralizer_order': 32, 'aut_label': '150.c1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '2.1', 'aut_weyl_index': 800, 'centralizer': '25.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.d1.a1', '30.d1.b1', '50.c1.a1', '75.a1.a1'], 'contains': ['300.b1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [7467, -1, 6063, -1, 7058, -1, 7053, -1], 'generators': [5], 'label': '600.157.150.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '150.c1.a1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110305825
    {'ambient': '600.157', 'aut_centralizer_order': 800, 'aut_label': '200.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 800, 'centralizer': '1.a1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '40.a1.b1', '40.b1.a1', '40.b1.b1', '100.a1.a1', '100.a1.b1', '100.b1.a1'], 'contains': ['600.a1.a1'], 'core': '200.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2527, 952, 2405, 7113, 4048, 3369, 2358, 3693], 'generators': [400], 'label': '600.157.200.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '200.a1.a1', 'normal_contained_in': ['40.a1.a1', '40.a1.b1'], 'normal_contains': ['600.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '200.a1.a1', 'projective_image': '200.42', 'quotient_action_image': '1.1', 'quotient_action_kernel': '200.42', 'quotient_action_kernel_order': 200, 'quotient_fusion': None, 'short_label': '200.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110305826
    {'ambient': '600.157', 'aut_centralizer_order': 160, 'aut_label': '300.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1600, 'centralizer': '5.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.a1.a1', '60.b1.a1', '100.a1.a1', '150.a1.a1'], 'contains': ['600.a1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [1949, -1, 1498, -1, 3192, -1, 2891, -1], 'generators': [20], 'label': '600.157.300.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '300.a1.a1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110305827
    {'ambient': '600.157', 'aut_centralizer_order': 160, 'aut_label': '300.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1600, 'centralizer': '5.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.a1.b1', '60.b1.b1', '100.a1.b1', '150.a1.a1'], 'contains': ['600.a1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [1949, -1, 2950, -1, 3192, -1, 1480, -1], 'generators': [38], 'label': '600.157.300.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '300.a1.b1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110305828
    {'ambient': '600.157', 'aut_centralizer_order': 64, 'aut_label': '300.b1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1600, 'centralizer': '25.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.c1.a1', '60.c1.b1', '60.d1.a1', '60.d1.b1', '100.b1.a1', '150.a1.a1', '150.b1.a1', '150.c1.a1'], 'contains': ['600.a1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [6138, -1, 5677, -1, 5625, -1, 5739, -1], 'generators': [2], 'label': '600.157.300.b1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '300.b1.a1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110305829
    {'ambient': '600.157', 'aut_centralizer_order': None, 'aut_label': '600.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '120.a1.b1', '120.b1.a1', '120.b1.b1', '200.a1.a1', '300.a1.a1', '300.a1.b1', '300.b1.a1'], 'contains': [], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2527, 1441, 2229, 6493, 3620, 3956, 3021, 3693], 'generators': [], 'label': '600.157.600.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '600.a1.a1', 'normal_contained_in': ['120.a1.a1', '120.a1.b1', '200.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '600.a1.a1', 'projective_image': '600.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110305830
    {'ambient': '600.157', 'aut_centralizer_order': 1, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '1600.10254', 'aut_weyl_index': 1, 'centralizer': '200.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '12.b1.a1', '20.c1.a1', '20.c1.b1', '20.d1.a1', '20.d1.b1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4784, 4017, 5173, 3821, 4161, 4103, 4522, 6364], 'generators': [2, 8, 120, 400], 'label': '600.157.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.c1.a1', '2.b1.a1'], 'normal_contains': ['8.a1.a1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110305831
    {'ambient': '600.157', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '40.12', 'aut_weyl_index': 40, 'centralizer': '100.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '10.b1.a1', '10.d1.a1', '15.a1.a1', '25.a1.a1'], 'core': '20.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [7623, -1, 7433, -1, 6374, -1, 6542, -1], 'generators': [1, 400, 2, 20, 8], 'label': '600.157.5.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}